How Much Force to Stop a Car on a Dime?

[robbondo]

Homework Statement

An advertisement claims that a particular automobile can "stop on a dime." What net force would actually be necessary to stop an automobile of mass m traveling initially at a speed of v in a distance equal to the diameter of a dime, which is d?

Homework Equations

F=ma

The Attempt at a Solution

Well I know that to stop the car you need to have a force equal to the force of the car at that point. And I know that if there is a distance and change in acceleration there must be some way to relate it to force. I'm just about completely lost though. I'm assuming there must be some simple way to solve this using Newtons laws. I think I just need a little direction.

 

[P3X-018]

Assuming constant acceleration, you can use the kinematic equation

$$a = \frac{v_2^2-v_1^2}{2d}$$

Where $v_2-v_1$ is the change in speed over the distance $d$, $a$ is the acceleration you seek.

 

[SGT]

Homework Statement

An advertisement claims that a particular automobile can "stop on a dime." What net force would actually be necessary to stop an automobile of mass m traveling initially at a speed of v in a distance equal to the diameter of a dime, which is d?

Homework Equations

F=ma

The Attempt at a Solution

Well I know that to stop the car you need to have a force equal to the force of the car at that point. And I know that if there is a distance and change in acceleration there must be some way to relate it to force. I'm just about completely lost though. I'm assuming there must be some simple way to solve this using Newtons laws. I think I just need a little direction.

Use conservation of energy. The kinetic energy of the car must be canceled by the work done by the force.