Question

If a car is speeding down a road at 40 miles/hour (\rm mph), how long is the stopping distance D_40 compared to the stopping distance D_25 if the driver were going at the posted speed limit of 25 \rm mph?

Answer 1

Let us suppose in both cases the braking force applied is the same; call it F.

Then by the Work-Energy theorem, the amount of work done, Work = Fd, where d is distance, must be equal to the change in energy, which here is all kinetic energy, KE.

Hence
Work = Change in KE
Fd = (1/2)mv^2

Now find \( d_{25} \) and \( d_{40} \) and compare them.