Answer:
23 m/s
Explanation:
First, find the time it takes for the car to fall 40 meters.
y = y₀ + v₀ t + ½ at²
0 = 40 + (0) t + ½ (-9.8) t²
0 = 40 − 4.9 t²
t = 2.89 s
Next, find the velocity needed to travel 65 meters in that time.
x = x₀ + v₀ t + ½ at²
65 = 0 + v₀ (2.89) + ½ (0) (2.89)²
v₀ = 22.75 m/s
Rounding to two significant figures, the car's initial speed was 23 m/s.
The likelihood of developing heart disease is correlated with high rates of
Final answer:
The development of heart disease is correlated with factors such as high cholesterol levels, obesity, and high blood pressure. Modifiable lifestyle choices, including diet and exercise, greatly influence cardiovascular health, while diabetes and family history also play significant roles.
Explanation:
The likelihood of developing heart disease is correlated with several factors. High cholesterol levels, particularly high amounts of "bad cholesterol", significantly increase the risk of cardiovascular diseases like coronary artery disease (CAD), where arteries narrow due to the buildup of plaques. Similarly, obesity, which involves having a very high percentage of body fat, especially around the abdomen, similarly elevates the risk for heart conditions.
Furthermore, high blood pressure makes the cardiovascular system work harder than normal, potentially leading to conditions like hypertension and contributing to heart disease. These are some of the modifiable factors affecting heart disease, in addition to lifestyle choices such as diet and exercise, which also play a crucial role in cardiovascular health.
It's important to note that preventing cardiovascular disease is possible by controlling these risk factors. Healthy lifestyle choices, such as quitting smoking, regular exercise, and a balanced diet, can lower a person's risk of developing heart disease. Additionally, being aware of the impact of diabetes and family medical history can help in managing and mitigating the risks associated with heart disease.
How is energy transformed from one form to another?
Options: Amplitude, crest, trough, wavelength
Which state of matter has a definite volume but a variable shape?
Liquid. Liquids have a definite volume but take up the shape of whatever they are in.
Happy to help!
City B is south of City A, and the 200 mile trip by car takes 4 hours. The cities are 120 miles apart in a straight line. What
is the velocity of a trip from City A to City B?
v=?
mph=?
Answer:
30 mph
Explanation:
Velocity is displacement over time. Displacement is the straight line distance between the starting point and ending point.
v = x / t
v = 120 mi / 4 hr
v = 30 mph
2. An automobile with an initial velocity of 6.3 m/s to the right accelerates
uniformly at the rate of 3 m/s2 to the right. What is the final velocity of the
automobile after it travels 52 meters to the right?
Answer:
18.8 m/s
Explanation:
Given:
v₀ = 6.3 m/s
a = 3 m/s²
Δx = 52 m
Find: v
v² = v₀² + 2a(x − x₀)
v² = (6.3)² + 2(3)(52)
v² = 351.69
v ≈ 18.8
The final velocity is approximately 18.8 m/s (round as needed).
What does mass, volume, and temperature measure?
Answer:
The metric system measures mass in grams or kilograms, distance in meters or kilometers, and volume in liters. It measures temperature in Kelvin or Celsius degrees instead of the Fahrenheit degrees used in the imperial system.
Answer:
The mass of a body is a measure of the resistance against a change of motion state of the body itself. That's why they usually call it "inertial mass" and is somehow an exclusive property that doesn't depend on "where" the body is in the space.
The volume of a body literally the amount of three-dimensional space that the body occupies.
The temperature of a body is a measure of the kinetic energy that the body has. The more the atoms of the body are moving, the hotter the body will be. Absolute zero (i.e. 0° K) is a state where all of the atoms of a body are motionless.
With reference to the international system of units, mass is measured in kilograms, volume in cubic metres and temperature in Kelvin.
The relationship among force, mass, and acceleration is stated in ___
A. The law of conversation of momentum
B. Newton's first law of motion
C. Newton's second law of motion
D. Newton's third law of motion
The relationship between force, mass, and acceleration is delineated in Newton's second law of motion. This rule, summarized as F = ma, implies that force equals mass times acceleration, and it describes how an object's velocity changes when an external force is applied.
Explanation:The relationship among force, mass, and acceleration is stated in C. Newton's second law of motion. Newton's second law states that force equals mass times acceleration often expressed as F = ma. In this equation, F stands for force, m for mass, and a for acceleration. This law describes how the velocity of an object changes when it is subjected to an external force. For example, if you push a skateboard (imparting a force), it will accelerate depending on both the force of your push (how much you pushed) as well as the mass of the skateboard.
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(V2 – V.), what do
6 Label In the equation a =
V, and v, represent?
In physics, specifically in thermodynamics and fluid dynamics, 'V' typically represents volume, which can be molar or specific volume depending on the context. The constant 'a' in the van der Waals equation accounts for intermolecular attraction, and its units vary with the type of volume 'V' used. These parameters are essential in equations of state to describe real gas behavior.
Explanation:In the context of physics, particularly in the study of thermodynamics and fluid dynamics, V often represents volume or specific volume. Considering the various equations and contexts provided, V can refer to molar volume or specific volume depending on the equation used. The volume variable is significant in equations of state, such as the ideal gas law and the van der Waals equation.
In the van der Waals equation, expressed as (P+a/V²) (V − b) = RT, 'a' represents the measure of attraction between particles within a gas, and 'b' accounts for the finite volume of gas particles, which is subtracted from the total volume V. Here, a essentially corrects for the intermolecular forces, and its units will vary depending on whether the volume V is specific or molar.
When seeking relationships between changing variables such as pressure (p) and volume V, constants a and b play crucial roles. These constants are parameters in the equation that relate pressure to volume, allowing for adaptations from ideal gas behaviors to more real-life scenarios where gases exhibit non-ideal characteristics.
What’s a Scientific law
Answer: scientific laws or the laws of science are statements that describe or predict a range of natural phenomena
Explanation:
How are NGC 1427A and U different? How are they the same?
Answer: NGC 1427A has no general shape, so it is an irregular galaxy. U has a bulge in the center and arms, so it is a spiral galaxy. They are similar in that both contain plenty of dust and gas. Both also have active star-forming sites.
Answer:
NGC 1427A has no specific shape, so it's an irregular galaxy. U has a spiral like shape so it's a spiral galaxy. They're similar because they both contain plenty of dust and gas. Both also have an active star-forming sites.
Explanation:
Put this as my answer and got it right
Which event happens when a star is forming
stars are made when atoms of light elements are compress under enough force for their nuclei to undergo fusion.
Positions B and D are 11.3 meters and 1.9 meters above the playing field, respectively. If the ball had a speed of 6.2 m/s in position B, what is its speed in position D?
Answer:
Speed of the ball in position D [tex]=14.92 \frac{m}{s}[/tex]
Explanation:
Given:
Position of B=11.3[tex]\text { meters }[/tex]
Position of D=1.9[tex]\text { meters }[/tex]
Velocity of B=6.2[tex]\text { meters }[/tex]
To Find:
Velocity of D
Solution:
According to the formula, Velocity is given as
[tex]V d=\sqrt{\left[V b^{2}+(2 \times g \times d y)\right]}[/tex]
[tex]V b[/tex]=Velocity of B
[tex]V d[/tex]=Velocity of D
g=acceleration due to gravity=9.8 m/s^2
[tex]d y[/tex]=Change in position of B and D
Substitute the all values in the above equation we get
[tex]d y=11.3-1.9[/tex]
[tex]V d=\sqrt{\left[6.2^{2}+(2 \times 9.8 \times(11.3-1.9))\right]}[/tex]
[tex]=\sqrt{[38.44+(2 \times 9.8 \times(9.4))]}[/tex]
[tex]=\sqrt{[38.44+(19.6 \times 9.4)]}[/tex]
[tex]=\sqrt{38.44+186.24}[/tex]
[tex]=\sqrt{222.68}[/tex]
[tex]=14.92 \frac{m}{s}[/tex]
Result :
The velocity of D is [tex]=14.92 \frac{m}{s}[/tex]
a ball is thrown inclined in to the air with a initial velocity of u. if it reaches the maximum height in 6 seconds , find the ratio to the distance travelled in 1 second to the 7th second... plzz help me
Answer:
11:1
Explanation:
At constant acceleration, an object's position is:
y = y₀ + v₀ t + ½ at²
Given y₀ = 0, v₀ = u, and a = -g:
y = u t − ½g t²
After 6 seconds, the ball reaches the maximum height (v = 0).
v = at + v₀
0 = (-g)(6) + u
u = 6g
Substituting:
y = 6g t − ½g t²
The displacement between t=0 and t=1 is:
Δy = [ 6g (1) − ½g (1)² ] − [ 6g (0) − ½g (0)² ]
Δy = 6g − ½g
Δy = 5½g
The displacement between t=6 and t=7 is:
Δy = [ 6g (7) − ½g (7)² ] − [ 6g (6) − ½g (6)² ]
Δy = (42g − 24½g) − (36g − 18g)
Δy = 17½g − 18g
Δy = -½g
So the ratio of the distances traveled is:
(5½g) / (½g)
11 / 1
The ratio is 11:1.
Which of these is important to gathering and interpreting scientific information?
A. Emotion
B. Legend
C. Religion
D. Logic
Answer:
D.) Logic
Explanation:
Definition:
the reasoning conducted or assessed according to strict principles of validity.
Hope this helps you out ; D
D. Logic.
Scientific information has been the consequence of scientific method, which is based on reason and observation. Hence, the gathering and interpretation of information in a scientific must be based on logic and reasoning, which are based on rules of inference, on what it is observed.
We conclude that correct choice is D.
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A student took a calibrated 200.0 gram mass, weighed it on a laboratory balance, and found it read 186.5 g. What was the student’s percent error?
The calculated percent error for the student who weighed a 200.0 g mass as 186.5 g is -6.75%, indicating that the measured value was lower than the actual value.
Explanation:The student's percent error is calculated using the formula [(observed value - true value) / true value] * 100. In this case, the observed value is the value measured by the student, which is 186.5 g. The true value is the actual weight of the object, which is 200.0 g. By substituting these values into the formula, we get percent error = [(186.5 g - 200.0 g) / 200.0 g] * 100, resulting in a percent error of -6.75%. This negative value indicates that the measured value is lower than the actual value.
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How do a neutron and a proton compare?
O A. The neutron has much less mass.
O
B. The neutron is farther from the nucleus.
O
C. They are equal in number in a neutral atom.
D. The proton has a positive charge, while the neutron has no charge.
Answer:
it would be d
Explanation:
because the neutron has a neutral charge so it has no charge at all
A neutron is electrically neutral and has a similar mass to a proton, which has a positive charge. While they both are part of the nucleus and contribute to an atom's mass, only the proton's charge affects the atom’s chemical properties. So the correct option is D.
Explanation:Comparing a neutron and a proton, option D is the correct answer: The proton has a positive charge, while the neutron has no charge. Both neutrons and protons reside in the nucleus of an atom and have approximately the same mass, which is about 1.67 × 10-24 grams, also known as one atomic mass unit (amu) or one Dalton. However, they differ significantly in terms of their electric charge. A proton has a positive charge (+1), essential in determining the atomic number and the chemical properties of an element. In contrast, a neutron is electrically neutral, carrying no charge at all, and contributes to the mass of an atom without affecting its electric charge. The number of protons and neutrons in the nucleus can vary; in a neutral atom, the number of electrons, which are negatively charged, is equal to the number of protons, balancing the net charge to zero.
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An elephant and a mouse would both have zero weight in gravity-free space. If they were moving toward you with the same speed, would they bump into you with the same effect? Explain.
The elephant and the mouse having zero weight in a gravity free space will not bump into you at the same effect.
Explanation:
When both are in a gravity free space, the weights are zero, as we know that the[tex]\text {weight of the body}=\text {mass of the body} \times \text {acceleration due to gravity}[/tex]
[tex]\text {here, the weight of elephant}=\text {mass of elephant } \times \text {zero gravti} y=zero[/tex]
[tex]\text {similarly,weight of mouse}=\text {mass of mouse } \times \text {zero gravity}=zero[/tex]
But when they will acquire the speed of same magnitude, say v, their different masses will acquire different momentum, which will make the difference in effect while bumping.
[tex]\text { momentum of elephant }=\text { mass of elephant } \times v[/tex] [tex]\text { momentum of mouse = mass of mouse } \times v[/tex]
And as we know [tex]\text { mass of elephant }>\text { mass of mouse }[/tex] Therefore, effect of impact by elephant will be more than that of mouse . An elephant breaking into you will take you back faster than a mouse in space hits you.
Two exactly similar wire of steel and copper are stretched by equal force.if the total elongation is 10cm.find how much each wire is elongated given young's modules for steel =2×10^10 N/M^2 and Young's modules for copper 2×10^10N/M^2.
Answer:
The copper wire stretches 6.25 cm and the steel wire stretches 3.75 cm.
Explanation:
Young's modulus is defined as:
E = stress / strain
E = (F / A) / (dL / L)
E = (F L) / (A dL)
Solving for dL:
dL = (F L) / (A E)
The wires have the same force, length, and cross-sectional area. So:
dL₁ + dL₂ = (FL/A) (1/E₁ + 1/E₂)
Given that dL₁ + dL₂ = 0.10 m, E₁ = 20×10¹⁰ N/m², and E₂ = 12×10¹⁰ N/m²:
0.10 = (FL/A) (1/(20×10¹⁰) + 1/(12×10¹⁰))
FL/A = 0.75×10¹⁰ N/m
Solving for dL₁ and dL₂:
dL₁ = (FL/A) / E₁
dL₁ = (0.75×10¹⁰ N/m) / (20×10¹⁰ N/m²)
dL₁ = 0.0375 m
dL₂ = (FL/A) / E₂
dL₂ = (0.75×10¹⁰ N/m) / (12×10¹⁰ N/m²)
dL₂ = 0.0625 m
The copper wire stretches 6.25 cm and the steel wire stretches 3.75 cm.
When you ride a roller coaster that makes sharp turns ,you feel yourself being pushed to one side . Use Newton’s first law of motion to explain this phenomenon
Explanation:
Newton's first law says that an object in motion stays in motion, and an object at rest stays at rest, until acted upon by an unbalanced force.
When a roller coaster makes a sharp turn, your body continues going straight until the seat belt pushes you and changes your direction. If the roller coaster didn't have seat belts, you'd slide off and continue moving straight.
According to Newton’s law of universal gravitation, which statements are true? As we move to higher altitudes, the force of gravity on us decreases. As we move to higher altitudes, the force of gravity on us increases. As we gain mass, the force of gravity on us decreases. As we gain mass, the force of gravity on us increases. As we move faster, the force of gravity on us increases.
According to Newton’s law of universal gravitation, as we move to higher altitudes, the force of gravity on us decreases and as we gain mass, the force of gravity on us increases both are the true statement.
Explanation:
Newton law of universal gravity extends gravity beyond the earth's surface. This gravity depends on the masses directly and inverse to the distance square between their centers.
[tex]F=G \frac{M \times m}{r^{2}}[/tex]
Where,
F – Force, G – gravitational constant, M and m – masses in kg, r – distance in meters.
Since force is proportional to the masses of interacting objects. If the mass of any one object increases, gravity between them also gets increased. When moving to higher altitude, force decreases as the distance is inverse proportion to gravity.
Why is it very important that only one variable be changed in a n experiment
Answer:
There should be only one manipulated variable within a scientific experiment so that the experimenter can be certain it is this variable which causes a pattern in the resultant data, if any exists at all. ... A variable within a scientific experiment is something that is changed
Explanation:
Answer:
There should be only one manipulated variable within a scientific experiment so that the experimenter can be certain it is this variable which causes a pattern in the resultant data, if any exists at all. ... A variable within a scientific experiment is something that is changed (i.e. it varies).yes here is correct
The atmosphere is held together by
A. the greenhouse effect
B. solar radiation
C. ozone
D. gravity
Answer:
D. gravity
Explanation:
Gravity keeps the atmosphere from escaping into space.
What is the acceleration of a softball if it has a mass of 0.50kg and hits the catchers glove with a force of 25N
Answer:
50 m/s²
Explanation:
From Newton's second law:
F = ma
25 N = (0.50 kg) a
a = 50 m/s²
The acceleration of a softball with a mass of 0.50kg and a force applied of 25N can be found by using Newton's second law of motion (F=ma). Upon rearranging the equation to solve for acceleration (a) and substituting the given values, we find that the acceleration is 50 m/s².
Explanation:To find the acceleration of the softball, we use Newton's Second Law of Motion, which states that the acceleration of an object is dependent upon the net force acting upon the object and the mass of the object, represented by the formula F = ma, where F is force, m is mass, and a is acceleration.
In this case, the force (F) applied on the softball is 25N and the mass (m) of the softball is 0.50kg. Rearranging the equation of Newton's second law to solve for acceleration (a), we get a = F/m.
Substituting the given values, we have a = 25N / 0.50kg. Solving the equation yields an acceleration (a) of 50 m/s².
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d A marathon runner runs at a average speed of 5.33 meters per second for the first
73600 seconds and then at a speed of 5.00 meters per second for the next 4200
seconds. What is the average speed of the marathon runner in meters per second?
F
5.1 m/s
G
2.6 m/s
H
0.4 m/s
J 1.06 m/s
Answer:
The average speed of the marathon runner is 5.15 meters per second
Explanation:
Lets revise the meaning of average speed
The average speed of an object is the total distance traveled by
the object divided by the time taken to cover that distance
A marathon runner runs at a average speed of 5.33 meters per second
for the first 3600 seconds
⇒ His speed = 5.33 m/s
⇒ For time = 3600 seconds
Then he runs at a speed of 5.00 meters per second for the next
4200 seconds
⇒ His speed is 5 m/s
⇒ For time 4200 seconds
Average speed = total distance ÷ total time
Lets find the total distance
Distance = speed × time
⇒ The 1st distance = 5.33 × 3600 = 19188 meters
⇒ The 2nd distance = 5 × 4200 = 21000 meters
⇒ Total distance = 19188 + 21000 = 40188 meters
Lets find the total time
⇒ Total time = 3600 + 4200 = 7800 seconds
⇒ Average speed = 40188 ÷ 7800 = 5.15 m/s
The average speed of the marathon runner is 5.15 meters per second
If the current through a resistor is cut in half, how does the power dissipated by the resistor change? (P=0VI=1^ 2 R= V^ 2 R )
Answer:
1/4
Explanation:
P = IV, and V = IR, so P = I²R.
If R is held constant, and I is cut in half, then power becomes:
P = (I/2)²R
P = 1/4 I²R
So the power reduces by a factor of 4.
The resistor change 1/4
P = IV, and V = IR, so P = I²R.
If R is held constant, and I is cut in half, then power becomes:
P = (I/2)²R
P = 1/4 I²R
So the power reduces by a factor of 4.
How does the resistance of the resistor exchange?The resistance of all substances modifications to their temperature modifications. If the temperature is diminished, resistance (commonly) declines. In fact, if cooled sufficiently, the material becomes a "superconductor" without huge resistance. Increasing the temperature (normally) will increase resistance.
If you boom the wide variety of lamps in a sequence circuit, there will be less modern-day. The lamps resist modern-day, so in case you placed extra lamps into the circuit, there may be more resistance. You can increase or lower the resistance in a circuit through the usage of a variable resistor.
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Since lower case m stands for both the prefix.milli and for unit for length meter, how do we tell which one is meant when they are used?
A: a prefix is never used alone. So a lone m (lower case) would refer to a unit, the meter (the SI metric unit of length.)
B: the prefix Comes before the unit, so mm (both lower case) would stand for millimeter.
C: the prefix comes before the unit, so mg (both lower case) would stand for milligram.
D: all of the other 3 answer choices.
Answer:
D: all of the other 3 answer choices
Explanation:
Milli- is a prefix, so a lowercase m in front of any other letter means milli-. For example, mm = millimeter and mg = milligram.
An m by itself means meters.
Answer:
D: all of the other 3 answer choices.
Explanation:
A: a prefix is never used alone. So a lone m (lower case) would refer to a unit, the meter (the SI metric unit of length.)
Above statement is true because here we can see that when prefix is placed before any SI unit then only we use it let say if we use only unit "m" then it is clearly assumed to be meter
B: the prefix Comes before the unit, so mm (both lower case) would stand for millimeter.
TRUE
Since prefix is always used before SI unit then we have to use the prefix like it is shown here for length. when we give unit as "mm" then it will show millimeter.
C: the prefix comes before the unit, so mg (both lower case) would stand for milligram.
TRUE
Since prefix is always used before SI unit then we have to use the prefix like it is shown here for mass. when we give unit as "mg" then it will show milligram.
9. Which of the following statements is true about scientific theories? (1 point)
Answer: D
Explanation:
We can immediately cross out A because theories and laws are completely different
We can then cross out B because laws have to go through many trials to prove them
C is wrong because laws and hypothesis are completely different
So that leaves us with D. Hope this helps!
Answer:
Scientific theories summarize patterns found in nature.
Explanation:
A scientific theory is an explanation of certain observed patterns. Scientific theories can be constantly improved, depending on the new phenomena observed that are studied through experiments that follow the scientific method. Therefore, a scientific theory allows to acquire an increasingly accurate knowledge about the mechanisms responsible for the patterns observed in nature.
002 10.0 points
A tennis ball with a speed of 10.1 m/s is
moving perpendicular to a wall. After striking
the wall, the ball rebounds in the opposite
direction with a speed of 8.3426 m/s.
If the ball is in contact with the wall for
0.00905 s, what is the average acceleration of
the ball while it is in contact with the wall?
Take “toward the wall” to be the positive
direction.
Answer in units of m/s2.
likel
and
1. ]
I don’t understand pleaseee help!
Answer:
-2040 m/s²
Explanation:
Taking toward the wall to be positive, the initial velocity is 10.1 m/s and the final velocity is -8.3426 m/s.
Average acceleration is the change in velocity over change in time.
a = Δv / Δt
a = (-8.3426 m/s − 10.1 m/s) / 0.00905 s
a = -2040 m/s²
The average acceleration of the ball while it is in contact with the wall is approximately −2034.39m/s².
The average acceleration of an object is defined as the change in velocity divided by the time interval during which the change occurs. In this case, the tennis ball hits the wall, changes its velocity, and rebounds. The change in velocity is the difference between its initial velocity and its final velocity after rebounding.
Given data:
Initial velocity (vi) = 10.1 m/s (moving toward the wall, positive direction)
Final velocity (vf ) = -8.3426 m/s (moving away from the wall, opposite direction)
Time interval (Δt) = 0.00905s
The change in velocity (Δv) is the difference between the final and initial velocities:
Δv=vf −vi
Δv = − 8.3426 m/s −10.1m/s=−18.4426m/s
Now, you can calculate the average acceleration (a) using the formula:
a= Δv / Δt
a= −18.4426m/s / 0.00905s
Calculating this:
a≈−2034.39m/s²
The negative sign indicates that the acceleration is directed toward the wall, which is what we expect since the ball is slowing down as it hits the wall.
So, the average acceleration of the ball while it is in contact with the wall is approximately −2034.39m/s².
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U. A hockey player takes a slap shot at a puck at rest on
the ice. The puck glides over the ice for 10 ft without
friction, at which point it runs over rough ice. The
puck then accelerates opposite its motion at a uniform
rate of - 20 ft/s2. If the velocity of the puck is 40 ft/s
after traveling 100 ft from the point of impact,
(a) what is the average acceleration imparted to the
puck as it is struck by the hockey stick? (Assume that
the time of contact is 0.01 s.) (b) How far in all does
the puck travel before coming to rest? (c) What is the total time the puck is in motion, neglecting contact time?
Answer:
a) 7200 ft/s²
b) 140 ft
c) 3.7 s
Explanation:
(a) Average acceleration is the change in velocity over change in time.
a_avg = Δv / Δt
We need to find what velocity the puck reached after it was hit by the hockey player.
We know it reached 40 ft/s after traveling 90 feet over rough ice at an acceleration of -20 ft/s². Therefore:
v² = v₀² + 2a(x − x₀)
(40 ft/s)² = v₀² + 2(-20 ft/s²)(100 ft − 10 ft)
v₀² = 5200 ft²/s²
v₀ = 20√13 ft/s
So the average acceleration impacted to the puck as it is struck is:
a_avg = (20√13 ft/s − 0 ft/s) / (0.01 s)
a_avg = 2000√13 ft/s²
a_avg ≈ 7200 ft/s²
(b) The distance the puck travels before stopping is:
v² = v₀² + 2a(x − x₀)
(0 ft/s)² = (5200 ft²/s²) + 2(-20 ft/s²)(x − 10 ft)
x = 140 ft
(c) The time the puck takes to travel 10 ft without friction is:
t = (10 ft) / (20√13 ft/s)
t = (√13)/26 s
The time the puck travels over the rough ice is:
v = at + v₀
(0 ft/s) = (-20 ft/s²) t + (20√13 ft/s)
t = √13 s
So the total time is:
t = (√13)/26 s + √13 s
t = (27√13)/26 s
t ≈ 3.7 s
The average acceleration or the total time will be:
(a) 7200 ft/s²(b) 140 ft(c) 3.7 sAccording to the question,
Velocity,
[tex]v^2 = 40 \ ft/s[/tex]Acceleration,
[tex]a = -20 \ ft/s^2[/tex](a)
As we know,
→ [tex]v^2=v_0^2+2a(x-x_0)[/tex]
By substituting the values, we get
→ [tex](40)^2=v_0^2+2(-20)(100-10)[/tex]
→ [tex]v_0^2=5200 \ ft^2/s^2[/tex]
→ [tex]= 20\sqrt{13} \ ft/s[/tex]
Now,
The average acceleration will be:
→ [tex]a_{avg} = \frac{\Delta v}{\Delta t}[/tex]
→ [tex]= \frac{20\sqrt{13}-0 }{0.01}[/tex]
→ [tex]= 2000\sqrt{13} \ ft/s^2[/tex]
→ [tex]= 7200 \ ft/s^2[/tex]
(b)
The distance will be:
→ [tex]v^2=v_0^2+2a(x-x_0)[/tex]
→ [tex](0)^2= 5200+2(-20)(x-10)[/tex]
→ [tex]0= 5200-40(x-10)[/tex]
→ [tex]x = 140 \ ft[/tex]
(c)
The time taken to travel 10 ft will be:
→ [tex]t = \frac{10}{20\sqrt{3} }[/tex]
[tex]= \frac{\sqrt{13} }{26} \ s[/tex]
The time taken over rough ice will be:
→ [tex]v = at+v_0[/tex]
[tex]0=-20t+20\sqrt{13}[/tex]
[tex]20t = 20\sqrt{13}[/tex]
[tex]t = \sqrt{13} \ s[/tex]
hence,
The total time taken will be:
→ [tex]t = \frac{\sqrt{13} }{26} +\sqrt{13}[/tex]
[tex]= \frac{27\sqrt{13} }{26}[/tex]
[tex]= 3.7 \ s[/tex]
Thus the above answers are correct.
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