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Constant Acceleration
Free Fall
Forces and Newton's Law
Kinetic Energy
Potential Energy



Free Fall
Conservation of Energy
Conservation of Momentum


Thinkquest Physics Library
Physics Zone
Multimedia Physics Studio

Classic Problem in Conservation of Energy

Here is an example of a typical question in the area of Conservation of Energy that students have difficulty solving:

A car starts moving from rest on the top of the hill. The hill is 5m high.
What is the speed of the car when it reaches the bottom of the hill?

Car, starting at rest, driving down a hill


In order to solve this problem we must find out the final speed of the car at the bottom of the hill right before it stops. We can do this by applying the law of conservation of energy, which states that the sum of initial kinetic and potential energies is equal sum of the final kinetic and potential energies. The following formula is used for conservation of energy:

Click on any part of the equation below to learn more about it.

After writing the formula we can plug in the information that is stated in the problem. The easiest way to do so is to plug the data into each part of the formula separately and try to simplify it.


In this problem we are given the following:

, because the car starts moving from rest which means that the initial velocity of the car is zero.

mghf = 0, because at the final moment the car is located at the bottom of the hill. In physics the bottom is equivalent to the ground level, which is considered as zero.

hi = 5 m

Step 2:

Plug the data into the formula:

We are going to cancel masses because they are the same on both sides of equation:

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Question: What is the speed of the car when it reaches the bottom of the hill?

Type your answer here: m/s