Problem 2-101 - Linear Kinematics - (a)

A car \((c)\) with one headlight burned out is traveling at a constant speed of \(18 \;m/s\) and passes a stopped police car \((p)\). The car is pursued immediately by the police cruiser, which has a constant acceleration of magnitude \(2.2 \;m/s^2.\)

(a) How far does the police cruiser travel before catching the other car?
(b) At what time will this occur? (Hint: Graphing may help to visualize this problem.)

Correct!

Solution A, depicting graphs indicating where the police cruiser intercepts the card with one head light

The acceleration of the police cruiser is constant in time, and that of the car is also constant but equal to zero.
Therefore the velocity of the cruiser increases linearly in time from zero, and that of the car remains constant.
The displacement of the car increases linearly in time and that of the cruiser increases with \(\mathrm{t^2.}\)

The cruiser catches up with the car at time:

graphs indicating where the police cruiser intercepts the card with one head light

(A)   \(t_1\)

(B)   \(t_2\)