Problem 2-101 - Linear Kinematics - Part 5 - (c)

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.)

Accumulated Solution

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

Displacement of the car
\(x_c = x_{0c} + v_{0c^t}\)

Displacement of the cruiser
\(x_p = x_{0p} + v_{0p} + ½ \;at^2\)


The condition for them being together is

\(x_p = x_c\)

In order for us to find the distance we must:
(A)   set \(x_p = x_c\) in the two equations and solve for \(t\)

(B)   set \(x_p = x_c = x\) and eliminate \(t\) between the two equations