# Homework Help: Speed of car dependent on what factors

1. Apr 24, 2012

### lilycat

1. The problem statement, all variables and given/known data
Disregarding friction, if a car was rolling down a hill, what would the speed of the car at the bottom of the hill, be dependent on? Either the height of hill, length of hill, rotational inertia or the acceleration due to gravity.

2. Relevant equations
Without friction wouldn't the length and height of the hill not matter?
Would the answer be different if friction was significant?

3. The attempt at a solution
If the height and the length don't matter then wouldn't it be the acceleration due to gravity?

2. Apr 24, 2012

### idrach55

Well, the speed of an object can be thought of as its Kinetic Energy (energy of motion). It sounds like a question relating to Conservation Of Energy in my opinion. Do you know about Conservation of Energy? If so, think about the energy the car has at the top of the hill (Hint: The energy the car has at the top must be equal to the energy it has at the bottom, if no energy was lost due to friction.) Try coming up with a equation that sets the initial energy at the top of the hill to the energy at the bottom of the hill, and algebraically solve for the velocity. Hope this helps.

- idrach55

3. Apr 24, 2012

### phinds

Are we to assume that the car STARTS at the top of the hill (that is, from rest) or that it has reached some sort of "terminal velocity" before the question is asked?

4. Apr 24, 2012

### lilycat

Okay I understand what you are saying. But if energy was lost due to friction what would happen to the problem?)

5. Apr 24, 2012

### idrach55

If friction was added to the problem, some of the energy the car had at the top of the hill would be lost due to friction by the time the car reached the bottom. The energy lost due to friction would be the work done by the friction. Thus you would end up with the Kinetic at the bottom equaling the Potential at the top (assuming the car started from rest) minus the work done by friction. That minus is there because the work done by friction can be thought of as negative (opposite direction) to the work done by gravity in going down the hill.