Problem 2-101 - Linear Kinematics - Part 4 - (b)

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.)


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

Displacement of the car

\(x_c = x_{0c} + v_{0c^t}\)


\(x_p = x_{0p} + v_{0p^t} + ½\;at^2\; \text{with} \; x_{0p} = 0\)

The condition for the two cars to meet is:
(A)   \(v_c = v_p\)

(B)   \(t = 0\)

(C)   \(x_c = x_p\)