# AP Physics C: Mechanics : Kinetic Energy

## Example Questions

### Example Question #1 : Kinetic Energy

A train car with a mass of 2400 kg starts from rest at the top of a 150 meter-high hill. What will its velocity be when it reaches the bottom of the hill, assuming that the bottom of the hill is the reference level.      Explanation:

The law of conservation of energy states: If the car starts at rest, then the initial kinetic energy = 0 J.

If the car ends at the reference height, the final potential energy = 0 J.

Subsituting these values, the equation becomes: The initial potential energy can be determined by: The final kinetic energy equation is: Substituting the initial potential energy and final kinetic energy into our modified conservation of energy equation, we get: ### Example Question #1 : Energy

An object has a mass of 5kg and has a position described by the given function: What is the object's kinetic energy after two seconds?     Explanation:

Kinetic energy is defined by the equation: Taking the derivative of the position function allows us to obtain the velocity function: We can now determine the velocity after two seconds: Now that we know our velocity, we can solve for the kinetic energy. ### Example Question #3 : Energy

An object starts from rest and accelerates at a rate of . If the object has a mass of 10kg, what is its kinetic energy after three seconds?     Explanation:

Kinetic energy is given by the equation: We can find the velocity using the given acceleration and time:  Use this velocity to find the kinetic energy after three seconds: ### Example Question #4 : Energy

A 120kg box has a kinetic energy of 2300J. What is its velocity?      Explanation:

The formula for kinetic energy of an object is: The problem gives us the mass and the kinetic energy, and asks for the velocity, so we can rearrange the equation: Use our given values for kinetic energy and mass to solve:  