All AP Physics C: Mechanics Resources
Example Question #4 : 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.
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 #5 : 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?
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 #6 : 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?
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 #3 : Kinetic Energy
A 120kg box has a kinetic energy of 2300J. What is its velocity?
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: