This question can be answered using conservation of energy. Having an understanding of the work-energy theorem allows us the knowledge that changing kinetic energy is a form of work, and that work can be a form of energy. In this particular question, the only force acting on the block to slow it down is the force of friction from the rough surface. As we know, work is equal to force times distance.

Because the block started with a certain amount of kinetic energy, and then is brought to a complete stop, all of that kinetic energy is transferred to work done by the force of friction over a distance of six meters.

Because the block had a velocity of  on a smooth surface and ends with a velocity of  at rest, we can calculate the change in kinetic energy.

The kinetic energy is completely converted to the work done by friction.

We can then use the first equation for work to determine the force of friction.

Because the force of friction is parallel to the displacement of the box, we can solve for the work done by friction using the following equation.

Now, we need to define the force of friction or .

In this formula,  equals acceleration. In this case, acceleration equals acceleration due to gravity in the x-direction; therefore, use the cosine function.

Insert the value of acceleration due to gravity for .

Now, we can solve for the work done by friction.

Power is equal to work/time. The work that child 1 is performing is also equal to the change in kinetic energy. When she goes from 2m/s to 4m/s, she is increasing her kinetic energy by mv².

This is the higest number of all the given scencarios.  To arrive at this conclusion, you must compare calculations for the other given scenarios.

Power is given by . Although the student exerts a force on the books during this time, they are not moved at all, so the displacement d is 0, and thus the power is also 0.

First we can find the intensity of light in Watts per square meter, when the light reaches the window, by using .

Assuming the light spreads out evenly in all directions, it has spread out over the area of a sphere of radius 3m by the time it reaches the window.

Multiplying this intensity times the area of the window gives the power (or energy per second) leaving the window.

In physics, power is often given the unit, W, or watts. In mechanics, a watt often represents the amount of work done over a unit of time, or Joules per second.

In electrostatics a watt is expressed as the amount of current times the voltage, or as the current squared times the resistance.

A Newton-meter is a measure of energy or work, and can be written as a Joule, and is therefore the correct answer because it is not a measure of power.

The power of an elevator can be determined using the equation , with  being the work done by the elevator, and  being the time in which energy is transferred. Using this, we can plug in the known values and solve for  the power.

To answer this question you need to know the definitions of work and power:

The units of work and power are Joules and watts, respectively. The passage states that the amount of time it takes to complete the task is same for both students; therefore, you can ignore the effects of time on power.

The passage also states that student Y applies less force. Since student Y applies less force, he has to expend less energy (work) than student X. This means that student Y also has to exert less power. A reduction in force will reduce work, and subsequently reduce power. We can thus conclude that student Y exerts less power than student X.

The first step is to find the force exerted by student X. The passage states that student Y exerts three times less force than student X; therefore, student X exerts three times more than student Y:

The second step is to find the amount of work done by student X.

Remember that student X directly lifts the boulder from point A to point B. This means that the distance the boulder travels is the vertical distance between point A and B ().

The question states that time for the entire process is . Since the time is the same for both students, power exerted by student X is:

The correct answer is .

This problem becomes much easier if we use the law of conservation of energy. Because there is no friction involved, all of the ball's potential energy was converted into kinetic energy when falling through the pendulum arc. As a result, the velocity at the bottom of the swing can be determined using the equation below.

Because the potential energy at the bottom of the swing is zero (relative to the starting point), and the velocity at the top is zero, we can simplify the equation.

Since the string is 10m long, we know that the lowest point will be 10m below the starting point.