Car B is traveling a distance dd ahead of car A. Both cars are traveling at 60 ft/s when the driver of B suddenly applies the brakes, causing his car to decelerate at ft/s^2. It takes the driver of car A 0.75 s to react (this is the normal reaction time for drivers). When he applies his brakes, he decelerates at 18 ft/s^2. Required:
Determine the minimum distance d between the cars so as to avoid a collision.

Explanation:

Using the kinematics equation to determine the velocity of car B.

where;

initial velocity

= constant deceleration

Assuming the constant deceleration is = -12 ft/s^2

Also, the kinematic equation that relates to the distance with the time is:

Then:

The distance traveled by car B in the given time (t) is expressed as:

For car A, the needed time (t) to come to rest is:

Also, the distance traveled by car A in the given time (t) is expressed as:

Relating both velocities:

t = 2.25 s

At t = 2.25s, the required minimum distance can be estimated by equating both distances traveled by both cars

i.e.

d + 104.625 = 114.75

d = 114.75 - 104.625

d = 10.125 ft