Auto stopping distance

Under optimum conditions on a dry road, the coefficient of friction may be as high as 0.8, so that you could decelerate at 0.8g = 0.8 x 9.8 m/s^2 = 7.8 m/s^2.
a. If you are traveling at 55 mi/h (24.6 m/s), how long will it take you to stop?
b. How far will you travel while stopping?

Solution:

All constant acceleration problems can be solved using the basic motion equations.

a. Using the basic motion equation

, or solving for t,

In the equation, v is the velocity at a chosen time t. In this problem the initial velocity is given, and you know that v=0 since it is the velocity at the time when you stop.

Examining the known and unknown quantities

leads to

b. The stopping distance may be calculated from the motion equation:

Alternatively, the distance may be calculated from the combined motion equation form which eliminates the time from the calculation.