Determine the stopping distances for an automobile with an initial speed of 95 km/h and human reaction time of 1.0 s : (a) for an acceleration a = -5.5 m/s2 : (b) for a = -6.6 m/s2

(a) 89.8 m

First of all, let's convert the initial speed from km/h into m/s:

During the reaction time of , the car still travels at constant speed, so it covers a distance of

Later, it slows down with acceleration

The distance covered in this second part can be found with the following equation:

where v=0 is the final speed of the car. Solving for S2,

So the total stopping distance is

(b) 79.2 m

This exercise is identical to the first part, except that this time the acceleration is

So, the distance covered while decelerating is

So the total stopping distance is