# Braking power and kinetic energy

I am currently stuck at a part of a problem i set myself. I am trying to create an equation for the stopping distance with respect to the force applied to the braking pads. I currently have two equations:

1) p=cv, braking power = constant * current velocity 2) e=kv^2, kinetic energy = constant * current velocity squared

i am trying to get an equation for the velocity with respect to time, or find the acceleration.

Any help would be greatly appreciated!

I am trying to create an equation for the stopping distance with respect to the force applied to the braking pads.

You can use the work energy theorem which states that the net work done on an object equals its change in kinetic energy, or

$$W_{net}=\frac{mv_{f}^2}{2}-\frac{mv_{i}^2}{2}$$

where $$f$$ and $$i$$ indicate final and initial velocities.

The net work equals the average force times the stopping distance. Since the final velocity is zero, we have

$$F_{ave}d=-\frac{mv_{i}^2}{2}$$

Where $$F_{ave}$$ is the average braking force on the vehicle and $$d$$ is the stopping distance of the vehicle.

The work is negative because the direction of the stopping force is opposite the displacement of the vehicle. Negative work means energy is removed from the car. In this case the brakes remove kinetic energy from the car by doing friction work and dissipating the energy as heat.

Hope this helps.