The position vector r describes the path of an object moving in the xy-plane. position vector point r(t) = ti + (ât2 + 7)j (1, 6) (a) find the velocity vector, speed, and acceleration vector of the object.
The velocity vector is v(t) = i + 2âtj, the speed is |v| = sqrt(1 + 4a^2t^2), and the acceleration vector is a(t) = 2âj.
Explanation:To find the velocity vector of the object, we need to take the derivative of the position vector with respect to time. The velocity vector is given by v(t) = dr/dt = i + 2âtj.
To find the speed of the object, we can calculate the magnitude of the velocity vector. The speed is given by the formula |v| = sqrt((i + 2âtj) dot (i + 2âtj)) = sqrt(1 + 4a^2t^2).
To find the acceleration vector of the object, we need to take the derivative of the velocity vector with respect to time. The acceleration vector is given by a(t) = dv/dt = 2âj.
The moon clearly exhibits a light and dark portion during most of the month except during full moon. What causes the dark portion of any phase to change in size, that is, become either more or less black ?
An element
is made up of compounds
is a homogenous mixture
can be divided by physical
cannot be divided into smaller substances by chemical means
You are learning about energy transformations in science class. Today, you are making a solar oven in science class. Your group's reward? You are going to use your solar oven to make s'mores: graham crackers, toasted marshmallows, and melted chocolate. When you have completed your oven, you get to eat the s'mores! Your oven converts solar energy into ___________ energy to make the s'mores.
A) cooked
B) heat
C) light
Eliminate
D) mechanical
Answer:
B) HEAT ENERGY
Explanation:
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When you have completed your oven, you get to eat the s'mores! Your oven converts solar energy into heat energy to make the s'mores. Therefore, option B is correct.
What is heat energy ?The movement of minuscule atoms, molecules, or ions in solids, liquids, and gases produces heat energy. From one thing to another, heat energy can be exchanged. Heat is the flow or transfer that occurs as a result of the temperature differential between two objects.
Radiation is used to cook the s'mores in the solar oven that is created in this exercise. When heat is passed between two objects (the sun and the s'mores) without having direct touch, this is known as radiation. Electromagnetic waves that move through the air transfer the heat.
Heat is created when visible and ultraviolet high frequency light transforms into low frequency infrared energy.
Thus, option B is correct.
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Describe how the amount of heat released or absorbed related to specific heat capacity and amount of it? A) Amount of heat absorbed or released is doubled if quantity is doubled. If a different substance with half the specific heat capacity is used, the amount of heat absorbed or released is doubled. B) Amount of heat absorbed or released is doubled if quantity is cut in half. If a different substance with half the specific heat capacity is used, the amount of heat absorbed or released is doubled. C) Amount of heat absorbed or released is doubled if quantity is doubled. If a different substance with half the specific heat capacity is used, the amount of heat absorbed or released is cut in half. D) Amount of heat absorbed or released is doubled if quantity is cut in half. If a different substance with half the specific heat capacity is used, the amount of heat absorbed or released is cut in half.
Answer:
The answer is C).
Explanation:
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The interior of earth consists almost entirely of _____ rock. felsic molten solid sedimentary
The higher u hold something above the ground? A. The less potential B. The more kinetic energy it has C. The more potential energy it has
You swing a bat and hit a heavy box with a force of 1500 n. the force the box exerts on the bat is
Light incident on a lake surface is partly reflected and partly refracted. How is the reflected ray different from the incident ray
The incident ray is a ray that hits the surface of the water. A reflected ray will always correspond to the incident ray and it is the light that is reflected by the surface of the water. Meaning, all rays that hit are incident rays, however, some are reflected rays.
A lens collects light and focuses it into a small spot. this increases the ________ of the light wave. w
A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s. using g = 9.8 m/s2 , the distance from launching to landing points is:
For a projectile, the distance of travel is determined by the horizontal velocity and the time spent in the air, which is dictated by the vertical velocity and gravity. We calculate the time from the equation t = (2*V0y)/g and then find the range from x = V0x * t.
Explanation:The distance from launching to landing for a projectile is determined by the horizontal motion because vertical motions regulate the time the projectile spends in the air but not the distance covered. Using the given initial vertical velocity (20 m/s) and horizontal velocity (30 m/s), and considering that the acceleration due to gravity, g, is -9.8 m/s2, the time in the air (t) can be calculated from the motion equation: t = (2*V0y)/g, where V0y is the initial vertical component of the velocity. Then, the range, or horizontal distance covered, x, can be found by multiplying this time by the horizontal component of the initial velocity, V0x: x = V0x * t, leading to the total distance the projectile traveled.
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Two hockey pucks with mass 0.1 kg slide across the ice and collide. Before the collision, puck 1 is going 15 m/s to the east and puck 2 is going 12 m/s to the west. After the collision, puck 2 is going 15 m/s to the east. What is the velocity of puck 1?
Final answer:
Using the conservation of momentum, the final velocity of puck 1 after the collision is determined to be 1.2 m/s to the west.
Explanation:
The student's question is about determining the velocity of puck 1 after a collision in an ice hockey game. Since momentum is conserved in collisions, we can use the law of conservation of momentum to find the answer. Puck 1 has a mass of 0.1 kg and is initially traveling at 15 m/s to the east, whereas puck 2, also 0.1 kg, is initially going 12 m/s to the west. After the collision, puck 2 is moving at 15 m/s to the east. We can set up the equation for conservation of momentum as follows:
Initial Momentum = Final Momentum
(m1 * v1_initial) + (m2 * v2_initial) = (m1 * v1_final) + (m2 * v2_final)
Plugging in the given values and solving for v1_final (velocity of puck 1 after the collision):
(0.1 kg * 15 m/s) + (0.1 kg * -12 m/s) = (0.1 kg * v1_final) + (0.1 kg * 15 m/s)
Simplifying the equation:
1.5 kg*m/s -1.2 kg*m/s = 0.1 kg * v1_final + 1.5 kg*m/s
Rearranging to solve for v1_final gives:
v1_final = (1.5 kg*m/s - 1.2 kg*m/s - 1.5 kg*m/s) / 0.1 kg
Calculating v1_final:
v1_final = -1.2 m/s
Therefore, after the collision, puck 1 is moving at a velocity of 1.2 m/s to the west.
If we mechanically squeeze a gas into a smaller volume, what happens to the pressure and temperature?
(A) The pressure and temperature both increase, but we can't predict how much each one will change.
(B) The pressure increases and the temperature decreases
(C) Only the pressure increases
If we mechanically squeeze a gas into smaller volume, the pressure and temperature both will increase, but we can't predict how much each one will change.
Answer: B
Explanation:
According to kinetic theory of gases, the pressure of a gas is inversely proportional to the volume of the gas. So as the volume is decreased, the pressure of the gas tends to increase.
As there is an increase in the pressure due to compression of volume by an external force, the temperature of the gas also increases as the external force or the work done will transfer its energy to the gas molecules leading to the increase in temperature.
The best example for this is heating of the mechanical air pumping machine for cycle Tyre.
During filling of air in cycle Tyre, we have to give extra mechanical energy in the pumping piston to compress the volume of air in the pumping machine and that gas get transferred to the Tyre.
But while pumping, the mechanical pumping machine gets heated up due to the mechanical work done on the piston.
This work done is transferred as heat to the molecules of gas thus increasing the gas temperature on decreasing the volume and also the pressure will be increased when volume is compressed mechanically.
Which sequence occurs from fastest to slowest on the earth's surface?
A.
lightning strike, lava flow, mountain formation
B.
lightning strike, mountain formation, lava flow
C.
lava flow, mountain formation, lightning strike
D.
mountain formation, lava flow, lightning strike
Answer:
a
Explanation:
You're using a wedge to split a log. you are hitting the wedge with a large hammer to drive it into the log. it takes a force of 1900 n to push the wedge into the wood. if the wedge moves 0.23 m into the log, how much work have you done on the wedge?
Answer: 437 J
Work done can be defined as the product of force and displacement. It is the work required to move an object to certain distance using a certain force.
[tex]work=force\times displacement[/tex]
It is given that:
[tex]Force=1900 N[/tex]
[tex]Displacement=0.23 m[/tex]
Then, [tex] work=1900N\times 0.23m = 437 N-m=437J [/tex]
Hence, the work done on the wedge to drive it into log is 437 J
A football is kicked from a tee at 12 m/s at 72° above the horizontal. What is the maximum height of the football
The maximum height of the football when kicked from a tee at 12 m/s at an angle of 72° above the horizontal is approximately 11.89 meters.
Explanation:To solve this problem, we will use the equation of motion that describes vertical displacement: h = vi sinθ t - 0.5gt2, where vi is the initial velocity, θ is the angle it was fired at, and g is the acceleration due to gravity. The maximum height is reached when the ball is momentarily stationary, in other words when the time, t, equals the time it takes for the ball to ascend (vi sinθ/g).
Substituting these values into our equation, we get: h = 12 sin(72°)*12 sin(72°)/9.8 - 0.5*9.8*(12 sin(72°)/9.8)2.
This results in a maximum height of approximately 11.89 meters.
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You're riding a unicorn at 25 m/s and come to a uniform stop at a red light 20m away. What's your acceleration?
The answer is -15.625m/s².
Acceleration is the change in velocity over a period of time. It can be computed using the formula:
[tex] a = \dfrac{vf-vi}{t} [/tex]
Where:
vf = final velocity
vi = initial velocity
t = time
Now let's see what was given in your problem:
The car was moving at 25m/s and then came to a stop. So initially it was moving and then it stopped. This means the final velocity will be 0m/s because it stopped moving.
But look at the problem, it shows no time. We need to solve for time from the time it moved till it reached the red light 20 m away.
Time can be computed using the kinematics formula:
[tex] d = \dfrac{vi+vf}{2} *t[/tex]
We just derive the formula from the equation by filling out what we know first.
[tex] 20m = \dfrac{25m/s+0m/s}{2}(t)[/tex][tex] 20m = 12.5m/s{2}(t)[/tex]
The time it took from the point it was moving till it stopped is 1.6s. We can now use this in our acceleration formula.
[tex] a = \dfrac{0m/s-25m/s}{1.6s} [/tex]
[tex] a = \dfrac{-25m/s}{1.6s} [/tex]
[tex] a = -15.625m/s^{2} [/tex]
Notice that the acceleration is negative. This means that the car decelerated or slowed down.
Answer:
My acceleration is 15.63 m/s² (slowing down)
Explanation:
The expression for the acceleration is equal:
[tex]v^{2} _{f} -v^{2} _{i} =2ax[/tex]
Where
vi = initial speed = 25 m/s
vf = final speed = 0
x = displacement = 20 m
Replacing and clearing the acceleration "a":
[tex]a=\frac{v^{2} _{f} -v^{2} _{i} }{2x} =\frac{0-25^{2} }{2*20} =--15.63m/s^{2}[/tex]
The negative sign of acceleration means that it is slowing down
Compare and contrast the dark zone of the ocean with the forest floor of a tropical rain forest.What living or nonliving factors affect these areas?
Understandably, the ocean floor receives very little sunlight, because of how far down it is and the way that water molecules scatter and absorb light. As a result, the organisms have many adaptations to help them survive even this harsh climate.
Similarly to the ocean floor, the bottom of a rain forest doesn't receive much sunlight either. The plants there have adapted to have huge leaves, so that they can get as much sunlight for photosynthesis as possible.
An ideal spring obeys hooke's law: f = −bikx. a mass of m = 0.3 kg hung vertically from this spring stretches the spring 0.13 m. the acceleration of gravity is 9.8 m/s 2 . calculate the value of the force constant k for the spring. answer in units of n/m
The force constant of the spring is calculated by dividing the force due to the mass hung from the spring by the stretch of the spring. The result is approximately 22.615 N/m.
Explanation:To calculate the force constant k of the spring according to Hooke's Law (F = -kx), we need to determine the restoring force due to the mass hung from the spring. The force exerted by the mass (m = 0.3 kg) due to gravity is F = mg, where g is the acceleration due to gravity (9.8 m/s2). Using the given stretch of the spring (x = 0.13 m), we can rearrange Hooke's law to solve for k:
F = kx
mg = kx
k = mg/x
Substituting the given values:
k = (0.3 kg)(9.8 m/s2)/(0.13 m)
k ≈ 22.615 N/m
Therefore, the force constant of the spring is approximately 22.615 N/m.
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One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 2.51 km. they start at the west side of the lake and head due south to begin with. (a) what is the distance they travel? (b) what is the magnitude of the couple's displacement? (c) what is the direction (relative to due east) of the couple's displacement?
The ____ value of the overflow style keeps the element at the specified height and width, but cuts off excess content.
a. hidden
b. visible
c. scroll
d. auto
Answer:
The correct answer is A. The hidden value of the overflow style keeps the element at the specified height and width, but cuts off excess content.
Explanation:
Hidden variable theories are interpretations of quantum physics, which means that a quantum mechanical system cannot be fully described by a wave function, but at least one additional variable is needed.
Hidden values would give unambiguous value to the properties of a quantum mechanical particle - position, amount of motion and energy - whether observed or not. During the evolution of quantum physics, hidden variables were advocated by, among others, Albert Einstein, but today, especially after the presentation of Bell's theorem, they have weak support among physicists. The only such theory that is still minimally shown with interest is Bohemian mechanics, which uses non-local hidden variables.
what are the inner planets relative distance from the sun
The image illustrates that as the distance between two objects increases, the force of gravity ____________. A) decreases. B) increases. C) remains the same. D) increases then decreases.
B; Decreases
Because,
The image illustrates that as the distance between two objects increases, the force of gravity decrease. The strength of gravity is affected by the distance between two objects as well as their masses
What force causes static cling? What two types of charges does this force have?
5.3 × 1012 kg satellite is 1,800 m from another satellite that has a mass of 3.5 × 108 kg. What is the gravitational force between the satellites? 3.82 × 104 N 6.87 × 107 N 5.72 × 1014 N 1.03 × 1018 N
The answer is: 3.82 × 10^4 N. Hope this helps!
A girl is standing still in the middle of a baseball field. The girl catches the baseball and begins to move in the same direction as the thrown ball. What type of collision is being described? inelastic, since the girl moves in the same direction as the thrown ball inelastic, since the girl moves in the opposite direction of the thrown ball elastic, since the girl moves in the same direction as the thrown ball elastic, since the girl moves in the opposite direction of the thrown ball
Answer:
inelastic, since the girl moves in the same direction as the thrown ball
Explanation:
When two bodies collide then after collision if two bodies separate from each other and move with two different velocities then this is an example of elastic collision.
While if two bodies collide and after collision they stick with each other and moves in same direction with same velocity then this is an example of perfectly inelastic collision.
So here in the given case ball is caught by the girl and that the ball and girl move together with same speed in the initial direction of motion of ball. This shows the situation of perfectly inelastic collision
So here correct answer will be
inelastic, since the girl moves in the same direction as the thrown ball
An air-gap parallel plate capacitor of capacitance c0 = 20 nf is connected to a battery with voltage v = 12 v. while the capacitor remains connected to the battery, we insert a dielectric (κ = 2.6) into the gap of the capacitor, filling one half of the volume as shown below. what is u, the energy stored in the this capacitor?
Answer:
3.7 * 10[tex]^{-5} J[/tex]
Explanation:
Thinking process:
Let the energy be calculated by the following:
[tex]U = \frac{1}{2}CV^{2}[/tex]
where V is the voltage applied across the load.
C is the capacitance
In case of a dielectric, the capacitance is given by the following equation:
[tex]C = kC_{0}[/tex]
where [tex]C_{0}[/tex] is the capacitance in vacuum. So, the energy stored becomes:
[tex]U = \frac{1}{2} (kC_{o})V^{2}[/tex]
Then, k = 2.6 , [tex]C_{0} = 20 nF[/tex], and V = 12 V
Therefore, in the problem, the energy stored becomes:
[tex]U = \frac{1}{2} (2.6 * 20*10^{-9}) (12)^{2} \\ = 3.7 * 10^{-5} J[/tex]
A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28 ∘ incline. after sliding down the 110-m long incline (on which the coefficient of kinetic friction is μk = 0.18), the snowboarder has attained a velocity v. the snowboarder then slides along a flat surface (on which μk = 0.15) and comes to rest after a distance x. part a use newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface.
Acceleration on the inclined plane and flat surface is different. The acceleration of snowboarding on the inclined plane is 3.05 m/sec² while on the flat surface is 1.4715 m/sec².
What is the friction force?It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N).
Mathematically it is defined as the product of the coefficient of friction and normal reaction.
(a)
On resolving the given force and accelertaion in the different components and balancing the equation gets.
Components in the x-direction
mgsina-F= ma
mgcosa=R
F=μR
F = μmgcosa
mg(sina-μcosa)=ma
a=g(sina-μcosa)
a=9.31(sin28°-0.18cos28°)
a= 3.05 m/sec²
Hence acceleration of snowboarding on the inclined plane is 3.05 m/sec²
(b)
According to Newton's third equation of motion;
v²=u²+2as
v²= (5)²+2×3.05×110
v=26.4 m/sec.
Fₓ×f= mgμ=ma
a=g×μ
a=9.81×0.15
a= 1.47 m/sec²
Hence acceleration on the flat surface is 1.4715 m/sec².
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Which describes Michael Faraday’s work with electricity and magnetism?
Answer:
C. He discovered electromagnetic induction after seeing a changing magnetic field generate an electric current.
Explanation:
A spring-loaded piston-cylinder device is filled with 0.35 kg of water vapor that is initially at 4 mpa and 4000c. initially, the spring exerts no force against the piston. the spring constant in the spring-force relationship is k = 0.75 and the piston diameter is d = 20 cm. the water now undergoes a process until its volume is one-half of the original volume. calculate the final temperature and the specific enthalpy of the water.
To accurately calculate the final temperature and the specific enthalpy of the water vapor in the given spring-loaded piston-cylinder device after the water volume is reduced to half, we'd require the use of steam tables or equations of state and a clear understanding of the thermodynamic process involved.
Explanation:The spring-loaded piston-cylinder device question given is based on the principles of thermodynamics and requires calculating the final temperature and the specific enthalpy of water after it undergoes a process where its volume is halved. To solve this problem, one can use the steam tables alongside the principles of thermodynamic processes involving an ideal gas or a real substance such as water, depending on the provided properties and the specified conditions.
To calculate the final temperature and specific enthalpy, we would need more details such as the properties of the water vapor at its initial state (using steam tables or equations of state, for example) and the characteristics of the thermodynamic process (constant pressure, isothermal, adiabatic, etc.). Moreover, if the properties are not sufficient to solve analytically, we might utilize software or further data from thermodynamic tables to aid in solving this question.
Without additional information about the specific heat capacities or the relationship between pressure and temperature for the water vapor, it is challenging to provide an accurate answer to the student's question.