Answer:
a) Minimum acceleration is [tex]a=2.31\frac{m}{s^{2} }[/tex].
b) It will take [tex]t_{f}=14.41s[/tex].
Explanation:
Let's order the information.
Initial velocity: [tex]v_{i}=0m/s[/tex]
Final velocity: [tex]v_{f}=33.3m/s[/tex]
Initial position: [tex]x_{i}=0m[/tex]
Final position: [tex]x_{f}=240m[/tex]
a) We can use velocity's equation:
[tex]v_{f}^{2} = v_{i}^{2} +2a(x_{f}-x_{i})[/tex]
⇒ [tex]a=\frac{v_{f}^{2}-v_{i}^{2}}{2(x_{f}-x_{i})}[/tex]
⇒ [tex]a=2.31\frac{m}{s^{2} }[/tex].
b) For this, equation for average acceleration will be helpful. Taking [tex]t_{i}=0[/tex] and having [tex]t_{f}[/tex] as the unknown time it becomes airborne:
[tex]a=\frac{v_{f}-v_{i}}{t_{f}-t_{i}} =\frac{v_{f} }{t_{f}}[/tex]
⇒ [tex]t_{f}=\frac{v_{f}}{a}=\frac{33.3\frac{m}{s}}{2.31\frac{m}{s^{2}}}[/tex]
⇒ [tex]t_{f}=14.41s[/tex].
To take off, the Cessna aircraft needs a minimum acceleration of 2.31 m/s² and it will take approximately 14.4 seconds to become airborne after a run of 240 meters.
To find the minimum constant acceleration required by a Cessna aircraft to become airborne after a takeoff run of 240 meters, and the time it takes to become airborne, follow these steps:
(a) Minimum Constant Acceleration
We use the kinematic equation: v² = u² + 2as, where:
v is the final velocity (33.3 m/s)u is the initial velocity (0 m/s, starting from rest)a is the accelerations is the distance (240 m)Substitute the known values:
[tex](33.3 m/s)^2 = 0 + 2a(240 m)\\1108.89 = 480a\\a = 2.31 m/s^2[/tex]
(b) Time to Become Airborne
We use the kinematic equation: v = u + at, where:
t is the timeOther variables are as previously definedSubstitute the known values:
[tex]33.3 m/s = 0 + (2.31 m/s^2)t\\t = 33.3 / 2.31\\t = 14.4 seconds[/tex]
A volleyball starts from rest and accelerates with an acceleration of 0.415 m/s2 while moving down a 9.00 m long inclined plane. When it reaches the bottom, the ball rolls up another plane, where, after moving 14.50 m, it comes to rest.
a) What is the speed of the ball at the bottom of the first plane?
m/s
b) How long does it take to roll down the first plane?
s
c) What is the acceleration along the second plane?
m/s2
d) What is the ball's speed 8.25 m along the second plane?
m/s
Answer:
a) v = 2.733 m/s
b) t = 6.58s
c) a = -0.415 m/s^2
d) v = 0.789 m/s
Explanation:
We can see it in the pics
Which equation below represents a generic equation suggested by a graph showing a hyperbola?
y = mx + b
y = k2
y = k/x
Answer:
y = k/x
Explanation:
y = k/x is a graph of a hyperbola that has been rotated about the origin.
The equation y = k/x represents a generic equation suggested by a graph showing a hyperbola
What is hyperbola?A right circular cone and a plane are intersected at an angle in analytical geometry to form a hyperbola, which is a conic section that intersects both cone halves. It results in two distinct unbounded curves that are mirror images of one another.
While a set of points in a plane that are equally spaced apart from a directrix or focus is known as parabolas. The difference of distances between a group of points that are present in a plane to two fixed points and is a positive constant is how the hyperbola is defined.
The general equation representing a hyperbola
y= k/x
Thus,a graph with a hyperbola suggests the equation y = k/x as a general equation.
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A test rocket is fired straight up from rest. The net acceleration is 20 m/s2 upward and continues for 4.0 seconds, at which time the rocket engines cease firing. What maximum elevation does the rocket reach?
Answer:
Maximum elevation, h = 160 meters
Explanation:
Initially, the rocket is at rest, u = 0
Acceleration of the rocket, [tex]a=20\ m/s^2[/tex]
Time, t = 4 s
We need to find the maximum elevation reached by the rocket. It can be calculated using second equation of motion as :
[tex]h=ut+\dfrac{1}{2}\times a\times t^2[/tex]
[tex]h=\dfrac{1}{2}\times 20\times (4)^2[/tex]
h = 160 meters
So, the maximum elevation reached by the rocket is 160 meters. Hence, this is the required solution.
Answer:
486.5 m
Explanation:
Initial velocity is zero as the rocket is fired from rest. u = 0.
Displacement of the rocket during this time:
s = ut +0.5 at²
s = 0+0.5 ×20×4²
s = 160 m
The final velocity at the end of 4 s is:
v = u + at
v = 0 + (20)(4)
v = 80 m/s
This will become the initial velocity for the next half of the motion.
At the maximum elevation, velocity is zero. v = 0
Acceleration due to gravity always acts downwards.
[tex]s=\frac{v^2-u^2}{2a}\\s=\frac{0-80^2}{2\times -9.8} = 326.5 m[/tex]
Thus, the maximum elevation that test rocket would reach is:
326.5 m + 160 m = 486.5 m
Two pieces of clay are moving directly toward each other. When they collide, they stick together and move as one piece. One piece has a mass of 300 grams and is moving to the right at a speed of 1 m/s. The other piece has mass 600 grams and is moving to the left at a speed of 0.75 m/s. What fraction of the total initial kinetic energy is lost during the collision?
Answer:
0.961
Explanation:
m1 = 300 g = 0.3 kg
u1 = 1 m/s
m2 = 600 g = 0.6 kg
u2 = - 0.75 m/s
Let after collision they move together with velocity v.
By using the conservation of linear momentum
Total momentum before collision = Total momentum after collision
m1 x u1 + m2 x u2 = (m1 + m2) v
0.3 x 1 - 0.6 x 0.75 = (0.3 + 0.6) v
0.3 - 0.45 = 0.9 v
v = - 0.166 m/s
Total initial Kinetic energy
[tex]K_{i}=0.5m_{1}u_{1}^{2}+0.5m_{1}u_{1}^{2}[/tex]
[tex]K_{i}=0.5\times 0.3\times 1\times 1+0.5 \times 0.6 \times 0.75 \times 0.75[/tex]
[tex]K_{i}=0.31875 J[/tex]
Total final Kinetic energy
[tex]K_{f}=0.5\left ( m_{1}+m_{2} \right )v^{2}[/tex]
[tex]K_{f}=0.5\times 0.9 \times 0.166 \times 0.166[/tex]
[tex]K_{f}=0.0124 J[/tex]
fraction of kinetic energy lost
[tex]\frac{K_{i}-K_{f}}{K_{f}}=\frac{0.31875-0.0124}{0.31875}=0.961[/tex]
Two pieces of clay are moves directly, and collide the momentum before and after the collision remain same. The fraction part of the total initial kinetic energy lost during the collision is 0.961.
What is kinetic energy?Kinetic energy is the energy of of the body, which it posses due to force of motion. The kinetic energy of a body is half of the product of mass times square of its velocity.
Given information-
The mass of piece one is 300 grams.
The mass of the second piece is 600 grams.
The speed of the first piece is 1 m/s.
The speed of the second piece is 0.75 m/s.
By the conservation of momentum, we know that the momentum of two body before the collision is equal to the momentum after the collision. As the momentum is product of mass times velocity. Thus,
[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]
Here, [tex]m_1,m_2[/tex] is the mass of body one, body 2 respectively and [tex]v_1,v_2[/tex] are the velocities of body one, body two before the collision respectively.
Put the values to find the value of velocity after the collision as,
[tex]0.3\times1+0.6\times0.75=(0.3+0.6)v\\v=-0.166 m/s[/tex]
Negative sine indicates the direction after the collision is changed.
Now the kinetic energy lost is the ratio of difference of initial kinetic energy and final kinetic energy to the initial kinetic energy.
Thus the kinetic energy lost is,
[tex]\Delta KE=\dfrac{k_i-k_f}{k_f}[/tex]
The kinetic energy is the half of the mass time square of its velocity. Thus,
[tex]\Delta KE=\dfrac{(\dfrac{1}{2}0.3\times0.1^2)-(\dfrac{1}{2}0.6\times0.75^2)}{\dfrac{1}{2}0.3\times0.1^2}\\\Delta KE=0.961[/tex]
Thus the fraction part of the total initial kinetic energy lost during the collision is 0.961.
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A telephone line hangs between two poles 14 m apart in the shape of the catenary , where and are measured in meters.
(a) Find the slope of this curve where it meets the right pole.
(b) Find the angle between the line and the pol
Final answer:
The slope of the catenary curve where it meets the right pole is -1. The angle between the line and the pole is -45 degrees.
Explanation:
The shape of the telephone line between two poles is known as a catenary. To find the slope where it meets the right pole, we can use the formula:
slope = -c/a
where 'c' is the distance from the vertex to the right pole and 'a' is half the distance between the poles. In this case, c = 7m and a = 7m. Substituting these values into the formula, we get:
slope = -7/7 = -1
Therefore, the slope of the curve where the line meets the right pole is -1.
To find the angle between the line and the pole, we can use the formula:
angle = arctan(slope)
Substituting the slope (-1) into the formula, we get:
angle = arctan(-1)
Using a calculator, we find that the angle is approximately -45 degrees.
Julian rides his bike uphill for 45 minutes, then turns around and rides back downhill. It takes him 15 minutes to get back to where he started. His uphill speed is 3 miles per hour slower than his downhill speed. Find Julian’s uphill and downhill speed.
Answer:
1.5mi/hr, 4.5mi/hr
Explanation:
Given:
45 min = 0.75h, 15 min = 0.25h
(1) 0.75v₁ = 0.25v₂
(2) v₁ = v₂ - 3
Solve for v₁ and v₂:
0.75(v₂ - 3) = 0.25v₂ = 0.75v₂ - 2.25 = 0.25v₂
0.5v₂ = 2.25
v₂ = 4.5
v₁ = 1.5
Answer:
uphill speed = 1.5 mph, downhill speed = 4.5 mph
Explanation:
We are asked to find Julian’s uphill speed and downhill speed. Let’s let r represent Julian’s uphill speed in miles per hour. In 45min=34hr, he rides uphill a distance rt=34r miles. Since his downhill speed is 3 miles per hour faster, we represent that as r+3. In 15min=14hr, he rides downhill a distance (r+3)t=r+34 miles. We can set these distances equal to find
34r=r+34
Multiplying both sides by 4 and then subtracting r from both sides yields
3r2r=r+3=3
Solving for r=32, Julian’s uphill speed is 1.5 miles per hour and his downhill speed is r+3=4.5 miles per hour.
A bullet fired horizontally hits the ground in 0.5 sec. If it had been fired with a much higher speed in the same direction, and neglecting air resistance and the earth’s curvature, it would have hit the ground in1. There is no way to tell from the information given.
2. less than 0.5 sec.
3. 0.5 sec.
4. more than 0.5 sec.
Answer:
3. 0.5 sec.
Explanation:
A bullet fired horizontally follows a projectile motion, which consists of two independent motions:
- A horizontal motion with constant speed
- A vertical motion with constant acceleration, g = 9.8 m/s^2, towards the ground
The time taken for the bullet to reach the ground can be calculated just by considering the vertical motion:
[tex]y(t) = h + v_{0y} t - \frac{1}{2}gt^2[/tex]
where y is the vertical position at time t, h is the initial height, and [tex]v_{0y}[/tex] is the initial vertical velocity of the bullet.
Since the bullet is fired horizontally, [tex]v_{0y}=0[/tex]. So the equation becomes
[tex]y(t) = h - \frac{1}{2}gt^2[/tex]
And the time that the bullet takes to reach the ground can be found by requiring y=0 and solving for t:
[tex]t=\sqrt{\frac{2h}{g}}[/tex]
As we can see, in this equation there is no dependance on the initial speed of the bullet: therefore, if the bullet is fired still horizontally but with a different speed, it will still take the same time (0.5 s) to reach the ground.
We have that for the Question "A bullet fired horizontally hits the ground in 0.5 sec. If it had been fired with a much higher speed in the same direction, and neglecting air resistance and the earth’s curvature, it would have hit the ground in1. There is no way to tell from the information given." it can be said that the time will remain the same
T=0.5
Option 2
From the question we are told
A bullet fired horizontally hits the ground in 0.5 sec. If it had been fired with a much higher speed in the same direction, and neglecting air resistance and the earth’s curvature, it would have hit the ground in1. There is no way to tell from the information given.
1. less than 0.5 sec.
2. 0.5 sec.
3. more than 0.5 sec.
Generally
When speed is increased and the Range also increased with respect to the speed
Therefore'
The time will remain the same
T=0.5
Option 2
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The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count C for a serving of food can be computed using the formula Upper C equals 4 h plus 9 f plus 4 p, where h is the number of grams of carbohydrate contained in the serving, f is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving. A serving of raisins contains 148 calories and 29 grams of carbohydrate. If raisins are a fat-free food, how much protein is provided by this serving of raisins?
Answer:
The raisins provide 8 grams of protein.
Explanation:
First wrote the information as a equation:
[tex]C=4h+9f+4p[/tex]
Where: C is calories, h carbohidrates, f fats and p protein
The information given for the raisin, 148 calories, 0 fat and 29 carbohidrates. That into a equation.
[tex]148=4(29)+9(0)+4p[/tex]
We clear p from the equation
14[tex]\frac{148-4(29)}{4} =p=8 gr[/tex]
Glycerin is poured into an open U-shaped tube until the height in both sides is 20cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20cm. The two liquids do not mix. What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?
Answer:
7.5 cm
Explanation:
In the figure we can see a sketch of the problem. We know that at the bottom of the U-shaped tube the pressure is equal in both branches. Defining [tex] \rho_A: [/tex] Ethyl alcohol density and [tex] \rho_G: [/tex] Glycerin density , we can write:
[tex] \rho_A\times g \times h_1 + \rho_G \times g \times h_2 = \rho_G \times g \times h_3 [/tex]
Simplifying:
[tex] \rho_A\times h_1 = \rho_G \times (h_3 - h_2) (1) [/tex]
On the other hand:
[tex] h_1 + h_2 = \Delta h + h_3 [/tex]
Rearranging:
[tex] h_1 - \Delta h = h_3 - h_2 (2) [/tex]
Replacing (2) in (1):
[tex] \rho_A\times h_1 = \rho_G \times (h_1 - \Delta h) [/tex]
Rearranging:
[tex] \frac{h_1 \times (\rho_A - \rho_G)}{- \rho_G} = \Delta h [/tex]
Data:
[tex] h_1 = 20 cm; \rho_A = 0.789 \frac{g}{cm^3}; \rho_G = 1.26 \frac{g}{cm^3} [/tex]
[tex] \frac{20 cm \times (0.789 - 1.26) \frac{g}{cm^3}}{- 1.26\frac{g}{cm^3}} = \Delta h [/tex]
[tex] 7.5 cm = \Delta h [/tex]
To find the difference in height between glycerin and alcohol in a U-tube, apply the principle of communicating vessels using their respective densities. Due to glycerin's higher density, its height in equilibrium will be lower than the alcohol's for equal pressures at the base of each arm of the tube.
Explanation:The difference in height between the top surface of the glycerin and the top surface of the alcohol can be determined by using the principle of communicating vessels and the densities of the two liquids. Since the two liquids do not mix, they will each exert a pressure at the bottom of their respective sides of the U-tube based on their densities and heights.
The density of glycerin is 1.26 g/cm3, and the density of ethyl alcohol is 0.789 g/cm3. Since the pressures at the bottom of the tubes must be equal and the pressure exerted by a column of liquid is given by the product of its density, gravitational acceleration, and height, we can set up the following equation:
density of glycerin × height of glycerin = density of alcohol × height of alcohol.
Using this relationship, we can calculate the heights. However, since the question states that the ethyl alcohol column's height is already 20 cm, we only need to verify if the glycerin column's height will remain at 20 cm or change. As glycerin is denser than ethyl alcohol, for the pressures to be equal, the height of the glycerin column should be less than the height of the alcohol column. However, additional information like the specific heights after the alcohol is added would be necessary to provide a numerical answer.
Light is a form of electromagnetic wave, containing oscillating electric and magnetic fields. The wave amplitude detector mentioned above shows how the electric field oscillates in time at the location of the probe. The amplitude of the wave at the location of the probe is equal to the maximum electric field measured. How does the amplitude of the wave depend on the distance from the source?
Answer:
the decrease in intensity is due to the conservation of energy in the wavefront.
Explanation:
Electromagnetic waves are transverse waves that comply with the principle of conservation of energy, these are formed by the variation of an electric and / or magnetic field and travels spherically from their point of origin.
By the principle of conservation of energy after the wave is emitted, the energy of it is distributed throughout the space, generally in spherical form. To conserve energy the density should decrease as the radius of the sphere increases, which is the inverse of the radius squared (1 / r²)
The previous decrease is observed in the decrease of the amplitude of the wave, since the intensity is the square of the electric field.
In summary, the decrease in intensity is due to the conservation of energy in the wavefront.
Final answer:
The amplitude of light decreases as the distance from the source increases due to the inverse square law, where the wave's energy spreads out over a larger area as it propagates.
Explanation:
The amplitude of an electromagnetic wave, such as light, is the maximum field strength of the electric and magnetic fields. In terms of the dependence of amplitude on the distance from the source, as light travels away from the source, the amplitude decreases. This happens because the wave's energy spreads out as the wave propagates, and because the energy of the wave is directly related to its amplitude, a reduction in energy with distance leads to a decrease in amplitude. If we consider a point source of light, the intensity (and therefore the amplitude) of the light diminishes in proportion to the square of the distance from the source, following the inverse square law.
The function s(t) represents the position of an object at time t moving along a line. Suppose s( 1 )=123 and s( 3 )=173. Find the average velocity of the object over the interval of time [1,3]?
Answer:
The average velocity is [tex]v_{average}=25[/tex].
Explanation:
The average velocity is calculated in the following way:
If [tex]s(t)[/tex] represents the position of an object at time [tex]t[/tex],
and [tex]s(t_{1})=a[/tex] ; [tex]s(t_{2})=b[/tex], the average velocity is defined in that interval as:
[tex]v_{average}= \frac{final.position-initial.position}{elapsed.time}=\frac{b-a}{t_{2}-t_{1}}[/tex]
Taking the data from the question:
[tex]v_{average}=\frac{173-123}{3-1}=\frac{50}{2}=25[/tex].
A car is driving at a speed of 59.0 km/h toward an intersection just as the light changes from green to yellow. The driver has a reaction time of 0.750 s and the magnitude of the braking acceleration of the car is 5.50 m/s2. Find the minimum distance xmin the car travels before coming to a stop after the light changes. (Express to three sig figs)
Answer:
The car travels 36.8 m before coming to stop after the light changes
Explanation:
The car moves at a constant speed of 59.0 km/h for 0.750 s before the driver hits the brake.
The equation for the position of an object moving at constant speed is:
x = x0 + v t
where:
x = position at time t
x0 = initial position
v = speed
t= time
Let´s consider the initial position as the position at which the driver sees the traffic light and decides to brake. That will make x0 = 0. Then, the position after 0.750 s will be:
x = 59.0 km/h * 0.750 s (1 h /3600 s) = 0.0123 km (1000 m / 1 km) = 12.3 m
while braking, the car has a negative acceleration, then, the speed is not constant. The position of the car will be given by the following equation:
x = x0 + v0 t + 1/2 a t² ( where a = acceleration and v0 = initial speed)
and the speed can be expressed as follows:
v = v0 + a t
from this equation, we can calculate how much time it takes the car to stop (v = 0):
0 = v0 + a t
-v0 = a t
-v0 / a = t
v0 is the speed of the car as the driver hits the brake (59.0 km/h) and "a" is the acceleration (5.50 m/s²) that will be negative because the car is losing speed. Then:
-59.0 km/h (1000 m / 1 km) (1 h / 3600 s) / (-5.50 m/s²) = 2.98 s
Now, we can calculate the position at this time to know the minimum distance the car travels before coming to stop:
x = x0 + v0 t + 1/2 a t²
now x0 will be the distance traveled after the driver sees the light but before braking ( 12.3 m). v0 will be the speed before braking, 59.0 km / h or 16.4 m/s. Then:
x = 12.3 m + 16.4 m/s * 2.98 s +1/2 (-5.50 m/s²) * (2.98 s)²
x = 36.8 m
Final answer:
The minimum distance the car travels before coming to a stop is 1225 m.
Explanation:
To find the minimum distance the car travels before coming to a stop, we need to consider the distance traveled during the driver's reaction time and the distance traveled while the car is decelerating.
First, we calculate the distance traveled during the reaction time using the equation:
distance = speed × time
distance = 59.0 km/h × 0.750 s = 44.3 m
Next, we calculate the distance traveled while decelerating using the equation:
distance = (initial velocity² - final velocity²) / (2 × acceleration)
distance = (59.0 km/h)² / (2 × 5.50 m/s²) = 1181 m
The minimum distance the car travels before coming to a stop is the sum of the distances traveled during the reaction time and while decelerating:
minimum distance = 44.3 m + 1181 m = 1225 m
Liquid methyl ethyl ketone (mek) flows through a pipe with an inner diameter of 2.067 inches at an average velocity of 0.48 ft/s. at the fluid temperature of 20°c the density of liquid mek is 0.805 g/cm3 and the viscosity is 0.43 centipoise [1 cp 1:00 103 kg/ m s]. without using a calculator, determine whether the flow is laminar or turbulent. show your calculations.
Answer:
Turbulent
Explanation:
The Reynolds number is:
Re = ρvL/μ
where ρ is the fluid density,
v is the velocity,
L is the characteristic length (for pipe, it's the diameter),
and μ is the dynamic viscosity.
Given:
ρ = 0.805 g/cm³
v = 0.48 ft/s = 14.63 cm/s
L = 2.067 in = 5.250 cm
μ = 0.43 cp = 0.0043 g/cm/s
Re = (0.805 g/cm³) (14.63 cm/s) (5.250 cm) / (0.0043 g/cm/s)
Re ≈ 14400
Flow is considered turbulent if the Reynolds number is greater than 4000. So this is turbulent.
On the moon the acceleration due to gravity is about 1/6 that on earth. If A golfer on the moon impacted the same initial velocity to the ball as she does on the earth, how much further with the ball go?
Answer: 6 times further
Explanation:
Initial velocity is the same that she uses on earth vertically and horizontally
Vertically we can say
V = -g t
If g is 1/6 earth gravity, then t is 6 times earth time.
Then, horizontally, with the same initial time, no incidence of gravity and knowing t
X= v t
Distance in the moon is 6 times distance in the earth.
What is the correct equation for calculating the average atomic mass for 3 isotopes? (pls be 100%of your answer pls no guessing)
Add all the masses together and divide by 3
Add all the protons together and divide by three
Multiply the percent abundance by each mass, add them up, and then divide by 3 Multiply the percent abudance by each mass and add them up
Answer:
The correct equation for measuring the average microscopic weight for 3 isotopes is multiply the rate of abundance by each weight and add them.
Explanation:
To calculate the average microscopic mass of element using weights and relative abundance we have to follow the following steps.
Take the correct weight of each isotope (that will be in decimal form)Multiply the weight of each isotope by its abundanceAdd each of the results together.This gives the required average microscopic weight of the three isotopes.
A motorcycle has a constant acceleration of 2.5 m/s2 . Both the velocity and acceleration of the motorcycle point in the same direction. How much time is required for the motorcycle to change its speed from (a) 21 to 31 m/s, and (b) 51 to 61 m/s?
A motorcycle has a constant acceleration of 2.5 m/s², the motorcycle takes 4 seconds to change its speed by 10 m/s.
The kinematic equation can be used to determine how long it will take the motorcycle to alter its speed. Initial velocity ([tex]v_0[/tex]), final velocity (v), acceleration (a), and time (t) are related by the following equation:
[tex]\[v = v_0 + at\][/tex]
Given that the acceleration (a) is 2.5 m/s² and both velocity and acceleration are in the same direction, we can use this equation to solve for time (t).
(a) Changing speed from 21 m/s to 31 m/s:
Initial velocity ([tex]\(v_0\)[/tex]) = 21 m/s
Final velocity (v) = 31 m/s
Acceleration (a) = 2.5 m/s²
31 = 21 + 2.5t
2.5t = 31 - 21
2.5t = 10
[tex]\[t = \dfrac{10}{2.5} = 4 \, \text{seconds}\][/tex]
(b) Changing speed from 51 m/s to 61 m/s:
Initial velocity ([tex]\(v_0\)[/tex]) = 51 m/s
Final velocity (v) = 61 m/s
Acceleration (a) = 2.5 m/s²
61 = 51 + 2.5
2.5t = 61 - 51
2.5t = 10
[tex]\[t = \dfrac{10}{2.5} = 4 \, \text{seconds}\][/tex]
Thus, in both cases, the motorcycle takes 4 seconds to change its speed by 10 m/s.
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The time required for the motorcycle to change its speed by 10 m/s, under a constant acceleration of 2.5 m/s², is 4 seconds in both scenarios: from 21 m/s to 31 m/s, and from 51 m/s to 61 m/s.
Explanation:In order to answer your question about the time required for the motorcycle to change its speed, we use the formula for acceleration, which is change in velocity divided by time (a = Δv/Δt). Thus, we can solve for time with Δt = Δv / a.
(a) For a speed change from 21 m/s to 31 m/s, Δv = 31 m/s - 21 m/s = 10 m/s. Substituting into the formula, we find Δt = 10 m/s / 2.5 m/s² = 4 seconds.
(b) For a speed change from 51 m/s to 61 m/s, Δv = 61 m/s - 51 m/s = 10 m/s. Again substituting into the formula, we find Δt = 10 m/s / 2.5 m/s² = 4 seconds.
Therefore, the time required for the motorcycle to change its speed by 10 m/s, under a constant acceleration of 2.5 m/s², is 4 seconds in both cases.
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The Hoover Dam in Nevada, supplied by Lake Mead, generates hydroelectric power for several western states, including the numerous lights in Las Vegas. What statement accurately explains the potential energy that Hoover Dam uses to generate this power? A) The large number of generators and height of the dam account for the potential energy. B) The depth of Lake Mead and the large number of generators account for the potential energy. C) The amount of water released through the dam and the dam's height account for the potential energy. D) The quantity of water flowing into Lake Mead from the Colorado River accounts for the potential energy. Submit
Answer:
C) The amount of water released through the dam and the dam's height account for the potential energy
Explanation:
The gravitational potential energy of an object is given by:
[tex]U=mgh[/tex]
where
m is the mass of the object
g is the acceleration of gravity
h is the height of the object relative to the ground
As we see from the equation, the potential energy depends on two factors related to the object:
- its mass
- its height above the ground
So for the water in the dam, its potential energy depends on
- the mass of the water (= the amount of water released)
- the height of the water (= the dam's height)
So the correct answer is
C) The amount of water released through the dam and the dam's height account for the potential energy
A vector has an x-component of 19.5m and a y-component of 28.4m. Find the magnitude and direction of the vector
Answer:
34.5 m at 55.5 degrees above the positive x-axis
Explanation:
Resolving a vector means finding its components along two perpendicular axis: most commonly, they are chosen as the x and y axis.
In this problem, we have a vector whose components are:
x -component: 19.5 m
y- component: 28.4 m
The two components are perpendicular to each other: this means that we can find the magnitude of the vector by using the Pythagorean theorem
[tex]v=\sqrt{v_x^2+v_y^2}=\sqrt{19.5^2+28.4^2}=34.5 m[/tex]
The direction, instead, can be found by using the following formula:
[tex]\theta=tan^{-1}(\frac{v_y}{v_x})=tan^{-1} (\frac{28.4}{19.5})=55.5^{\circ}[/tex]
The concentration of the appetite-regulating hormone ghrelin is about 1.3 × 10-10 M in the blood of a fasting person.How many molecules of ghrelin are in 1 L of blood?a) 2.2 × 10-34b) 1.3 × 10-10c) 7.8 × 1013d) 4.6 × 1033
Answer:
There are 7.8 x 10¹³ molecules ghrelin in 1 l blood
Explanation:
Molarity (M) means the number of moles of a solute in one-liter solution. Then, 1.3 x 10⁻¹⁰ M means that there are 1.3 x 10⁻¹⁰ moles of ghrelin in 1 l of blood.
Since 1 mol of something are 6.022 x 10²³ something, then:
1.3 x 10⁻¹⁰ mol ghrelin * 6.022 x 10²³ molecules ghrelin / 1 mol ghrelin
= 7.8 x 10¹³ molecules ghrelin
Acceleration problem
Show work plz
Answer:
The answer to your question is: vo = 25 m/s
Explanation:
data
a = -7.5 m/s²
d = 42 m
vf = 0 m/s
vo = ?
Formula
vf² = vo² - 2ad
Substitution
0² = vo² - 2(7.5)(42)
We clear vo from the equation
vo² = 2(7.5)(42)
vo² = 630 simplifying
vo = 25 m/s result
Two identical closely spaced circular disks form a parallel-plate capacitor. Transferring 2.1×109 electrons from one disk to the other causes the electric field strength between them to be 1.5×105 N/C .
What are the diameters of the disks?
Answer:
[tex]d = 0.018 m[/tex]
Explanation:
Charge on the plates of the capacitor due to transfer of electrons is given as
[tex]Q = Ne[/tex]
here we know that
[tex]N = 2.1 \times 10^9[/tex]
so we have
[tex]Q = (2.1 \times 10^9)(1.6 \times 10^{-19})[/tex]
[tex]Q = 3.36 \times 10^{-10} C[/tex]
now we have electric field between the plates is given as
[tex]E = \frac{Q}{A\epsilon_0}[/tex]
here we have
[tex]1.5 \times 10^5 = \frac{3.36 \times 10^{-10}}{A(8.85 \times 10^{-12})}[/tex]
[tex]A = 2.53 \times 10^{-4} m^2[/tex]
now we have
[tex]A = \frac{\pi d^2}{4}[/tex]
[tex]2.53 \times 10^{-4} = \frac{\pi d^2}{4}[/tex]
[tex]d = 0.018 m[/tex]
The the diameters of the disks of the parallel-plate capacitor are 0.018 m.
Given parameters:
Number of electron transferring from one disk to another: n = 2.1×10⁹.
Electric field strength: E = 1.5×10⁵ N/C .
We have to find: the diameters of the disks: d = ?
Charge of an electron is: e = 1.6 × 10⁻¹⁹ C.
So, charge transferring from one disk to another:
Q = ne = 2.1×10⁹×1.6 × 10⁻¹⁹ C = 3.36×10⁻¹⁰ C
For parallel-plate capacitor: electric field strength is given by:
E = Q/ε₀A
Where:
A = area of each disks = πd²/4
ε₀ = permittivity of free space = 8.85 × 10⁻¹² Si units.
Hence,
A = Q/ε₀E
⇒ πd²/4 = Q/ε₀E
⇒ d = √( 4Q/πε₀E)
Putting numerical values we get:
d = √( 4 × 3.36×10⁻¹⁰/π×8.85 × 10⁻¹² × 1.5×10⁵ ) m.
= 0.018 m.
Hence, the diameters of the disks are 0.018 m.
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A man finds that he has a mass of 100.6 kg. He goes on a diet, and several months later he finds that he has a mass of 96.4 kg. Express the mass 100.6 kg in scientific notation.
The question is weird. It doesn't matter whether it was a man or a woman, or whether he went on a diet, or whether he gained or lost mass or stayed the same, or what his mass was later. In fact, it doesn't even matter WHAT the number 100.6 represents. The answer would be the same in any case.
100.6 = 1.006 x 10^2
If a man finds that he has a mass of 100.6 kg. He goes on a diet, and several months later he finds that he has a mass of 96.4 kg, then his mass in the scientific notation would be 1.006 × 10² kg.
What are significant figures?In positional notation, significant figures refer to the digits in a number that is trustworthy and required to denote the amount of something, also known as the significant digits, precision, or resolution.
Only the digits permitted by the measurement resolution are trustworthy, therefore if a number expressing the result of a measurement (such as length, pressure, volume, or mass) has more digits than the number of digits permitted by the measurement resolution, only these can be significant figures.
Thus, If a man discovers that he weighs 100.6 kg. He starts a diet, and after a few months discovers he weighs 96.4 kg, his mass would be written as 1.006 10² kg in the scientific notation.
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What is the maximum number of atoms that can be bonded in an ionic bond
A maximum of four bonds can be used between two atoms.
Explanation:
Ionic bond is one of the strongest bond used in chemical reaction where the valence electrons are bonded and shared between the atoms. Sometimes four covalent bonds between two atoms might make them unstable as the bonds are formed in their outermost shell to make them to form or complete a total of 8 in their shell. For example carbon has 3 as maximum.
A 23.0 kg block at rest on a horizontal frictionless air track is connected to the wall via a spring. The equilibrium position of the mass is defined to be at x=0. Somebody pushes the mass to the position x= 0.350 m, then lets go. The mass undergoes simple harmonic motion with a period of 4.10 s. What is the position of the mass 3.403 s after the mass is released?
Answer:
Explanation:
We use the harmonic motion position equation:
[tex]x(t) = A\cos(\omega t+\phi)[/tex]
where A = 0.350 and for t = 0
[tex]x(0) A = A\ cos(\phi)[/tex]
so: [tex]\phi = 0[/tex]
and also:
[tex]\omega = \frac{2\pi}{T} = \frac{2\pi}{4.10} = 1.532 rad/s[/tex]
so we have:
x(t)=0.350cos(1.532 t)
For t = 3.403 s
x(3.403)=0.350cos(1.532 (3.403)) = 0.348 m
The block attached to a spring is undergoing simple harmonic motion. By fitting the provided variables into the displacement equation for such a motion, it is found that the block's position 3.403 seconds after release is -0.279 meters.
Explanation:The problem describes a scenario involving simple harmonic motion (SHM). For such a motion, the displacement, x(t) from equilibrium position could be expressed as x(t) = A * cos(ωt + φ), where 'A' is the amplitude, 'ω' = 2π/T is the angular frequency, 'T' is the period of the motion, t is the given time, and 'φ' is the phase constant. Since the motion begins at the amplitude, φ = 0.
Amplitude given is 0.35 m and period is 4.10 s. Thus, 'ω' = 2π / 4.10 = 1.5 rad/s. Putting these values into the displacement equation, x(t) = 0.350 m * cos(1.5 rad/s * 3.403 s) = -0.279 m. Therefore, the position of the mass 3.403 s after it's released is -0.279 m.
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A ball is thrown vertically upward from the top of a building 80 feet tall with an initial velocity of 64 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s=80+64t-16t^2.a) After how many seconds does the ball strike the ground?b) After how many seconds does the ball pass the top of the building on its way down?
Answer:
a) [tex]t=6.37s[/tex]
b) [tex]t=3.3333s[/tex]
Explanation:
The knowable variables are the initial hight and initial velocity
[tex]s_{o}=80ft[/tex]
[tex]v_{os}=64ft/s[/tex]
The equation that describes the motion of the ball is:
[tex]s=80+64t-16t^{2}[/tex]
If we want to know the time that takes the ball to hit the ground, we need to calculate it by doing s=0 that is the final hight.
[tex]0=80+64t-12t^{2}[/tex]
a) Solving for t, we are going to have two answers
[tex]t=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
a=-16
b=64
c=80
[tex]t=-1.045 s[/tex] or [tex]t=6.378s[/tex]
Since time can not be negative the answer is t=6.378s
b) To find the time that takes the ball to pass the top of the building on its way down, we must find how much does it move too
First of all, we need to find the maximum hight and how much time does it take to reach it:
[tex]v_{y}=v_{o}+gt[/tex]
at maximum point the velocity is 0
[tex]0=64-32.2t[/tex]
Solving for t
[tex]t=1.9875 s[/tex]
Now, we must know how much distance does it take to reach maximum point
[tex]s=0+64t-16t^{2} =64(1.9875)-12(1.9875)^{2} =80ft[/tex]
So, the ball pass the top of the building on its way down at 160 ft
[tex]160=80+64t-16t^{2}[/tex]
Solving for t
[tex]t=2s[/tex] or [tex]t=3.333s[/tex]
Since the time that the ball reaches maximum point is almost t=2s that answer can not be possible, so the answer is t=3.333s for the ball to go up and down, passing the top of the building
Answer:
(a) 5 s
(b) 4s
Explanation:
height of building, s = 80 feet
The equation of motion is given by
[tex]s=80+64t-16t^{2}[/tex]
(a) Let it takes t time to reach the ground. A it reach the ground, s = 0
So, put s = 0 in the given equation, we get
[tex]0=80+64t-16t^{2}[/tex]
[tex]t^{2}-4t-5=0[/tex]
(t + 1)(t - 5) = 0
t = -1 s, t = 5 s
As time cannot be negative, so t = 5 s
Thus, the time taken by the ball to reach the ground is 5 s.
(b) Let it crosses the building in t second, s put s = 80 feet in the above equation, we get
[tex]80+64t-16t^{2}=80[/tex]
t(4 - t)= 0
t = 0s or t 4 s
So, it takes 4 second to cross the building.
Which equation describes the fastest runner?
A. distance=0.5⋅time
B. distance=0.33⋅time
C. distance=time
D. distance=2⋅time
The equation which has the fastest runner is Distance = 2 * Time.
The correct answer is Option D.
Given data:
The equation that describes the fastest runner among the given options is D. distance = 2⋅time.
This equation suggests that the distance traveled by the runner is directly proportional to twice the time taken. In other words, if two runners start at the same time and one of them has a faster speed, they will cover a greater distance in the same amount of time. This equation aligns with the principles of speed and distance in physics.
Option D reflects that the distance covered by a runner is determined by the product of time and speed. When the speed is greater (as indicated by the coefficient of 2), the distance covered in a given time will be larger, making this equation representative of the fastest runner. The other options, A, B, and C, do not consider the concept of speed and do not accurately describe the behavior of a fastest runner in relation to distance and time.
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Final answer:
The fastest runner is described by Equation D, which represents a speed of 2 meters per second (2 m/s), as it has the highest coefficient of time in the distance = speed × time equation.
Explanation:
The equation that describes the fastest runner is the one where the coefficient of time (t) in the distance = speed × time equation is the greatest, as this coefficient represents the speed of the runner. The faster the runner, the greater the distance they would cover in a given time. Comparing the given equations:
A. distance = 0.5×time (speed of 0.5 m/s)
B. distance = 0.33×time (speed of 0.33 m/s)
C. distance = time (speed of 1 m/s)
D. distance = 2×time (speed of 2 m/s)
The fastest runner is described by Equation D, where the distance is twice the time, indicating a speed of 2 meters per second (2 m/s).
Newton’s first law of motion was a giant leap forward in scientific thought during Newton’s time. Even today, the idea is sometimes difficult at first for people to understand.
Which statement is the best example of an object and motion that would make it hard for people to believe Newton’s first law?
a. A rolling ball eventually slows down and comes to a stop.
b. A wagon must be pushed before it begins to move.
c. The heavier the load in a cart, the harder the cart is to turn.
d. A box does not move when pushed equally from opposite sides.
Answer: B
Explanation:
Newton's first law it's law of inertia.
An object at rest will remain at rest (or an object in motion in a straight line at a constant velocity will remain that way) unless it is acted by an unbalanced force.
In A for the ball to slow down and stop, an external force (like friction with air or the floor) needs to be taken in consideration.
In B we can see how we need to make a force on the wagon to make it move.
In C we have an other Newton 's law, force equals mass times acceleration (2nd law)
In D we can see how it does not move because the forces on the box are balanced.
Answer: a. A rolling ball eventually slows down and comes to a stop.
How long will it take a car to go from a complete stop to 450 m/s if it is accelerating at 60.5 m/s2?
Answer:
7.44 seconds
Explanation:
v = at + v₀
where v is the final velocity,
v₀ is the initial velocity,
a is the acceleration,
and t is time.
Given v = 450 m/s, v₀ = 0 m/s, and a = 60.5 m/s²:
450 = (60.5)t + 0
t ≈ 7.44
It takes approximately 7.44 seconds.
A 10-L drum of ether at 18°C is open to the atmosphere {P = 760 torr) and contains 6 L of liquid. The top is sealed and the drum dented so that it now has an 8-L capacity. If the vapor pressure of ether at 18°C is 400 torT, what is the pressure inside the dented, sealed drum?
Answer:
the final pressure = 1120 torr
Explanation:
In the starting, when a 10-L drum consist 6 L of ether at 18°C
Volume of gas [tex]= ( 10 L - 6 L ) = 4 L[/tex]
Total pressure of gas which is equal to Atmospheric Pressure = 760 Torr
vapor pressure of liquid (ether) = 400 Torr
vapor pressure of air
[tex] = ( 760 Torr - 400 Torr ) = 360 Torr[/tex]
when the drum top is sealed & dented to 8 L capacity
Volume of gas [tex] = ( 8 L - 6 L ) = 2 L[/tex]
Total pressure of gasses
[tex] = 760 Torr x ( 4 L / 2 L ) = 1560 Torr[/tex]
vapor pressure of ether [tex]= 400 Torr x 2 = 800 Torr[/tex]
vapor pressure of air [tex]= 360 Torr x 2 = 720 Torr[/tex]
But some of the liquid (ether) vapor will condensed into liquid just to maintain the vapor pressure of ether at 400 Torr )
therefore, the final pressure
[tex]= [ 400\ Torr (ether ) + 720\ Torr (air) ] = 1120 Torr[/tex]
Answer:
final total pressure is 1120 torr
Explanation:
given data
volume v1 = 10 L
volume v2 = 6 L
temperature = 18°C
atmosphere pressure P = 760 torr
volume v3 = 8 L
vapor pressure = 400 torr
to find out
pressure inside the dented
solution
we know here at 6 L volume by small amount of vaporize no temperature will change
and
gas volume in drum is = 10 - 6 = 4L
and
atmosphere pressure = total pressure inside drum
and
partial pressure of air is = 760 - 400
partial pressure of air is = 360 torr
so
at 8 L volume sealed and sealed then gas volume inside drum is
gas inside = 760 × [tex]\frac{4}{2}[/tex]
gas inside = 1560 torr
so partial pressure either side is
partial pressure = 2× 400 = 800 torr
partial pressure = 2× 360 = 720 torr
so we keep vapor pressure here 400 torr
so
final total pressure = 400 + 720
final total pressure is 1120 torr
Two students are arguing over the differences between speed and velocity. One student says,
“Speed is a scalar because it describes how fast an object is traveling. Velocity is a vector because it tells how fast and in what direction an object is traveling.” Which of the following statements is correct? (AKS 1b3 DOK 3)
Question 3 options:
The student’s understanding of all four terms (speed, velocity, scalar, and vector) is correct.
The student’s understanding of speed and velocity is correct but their understanding of scalar and vector is incorrect.
The student’s understanding of all four terms (speed, velocity, scalar, and vector) is incorrect.
The student’s understanding of speed and velocity is incorrect but their understanding of scalar and vector is correct.
Answer: The student’s understanding of all four terms (speed, velocity, scalar, and vector) is correct.
Explanation:
Let's start by explaining that a vector is one that has a numerical value along with its units (called a module) and a direction, while a scalar is only determined with a number and its corresponding units, without direction.
Then, speed is the distance an object travels in a given time. That is, it only takes into account the distance traveled, dividing it by time to know how fast it moves, therefore it is a scalar.
Instead, velocity refers to the time it takes for an object to move in a certain direction. So, by involving the direction of movement, velocity is a vector.
In short, the speed does not take into account the direction of the object, while the velocity does.
Therefore, as the student understands this four concepts, the correct option is:
The student’s understanding of all four terms (speed, velocity, scalar, and vector) is correct.