Problem 2-101 - Linear Kinematics - Part 3 - (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.)


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

Since the acceleration of the car is zero (constant velocity) and we take \(x\) as measured from the position where the two cars are together \((x_{0_c} = 0)\), then

\(x_c = x_{0c} + v_{c^t}, \text{with} \; x_{0c} = 0 \\ \text{or} \; x_c = v_{c^t}\)

The expression relating the cruiser's displacement\((x_p)\) to the time \((t)\) is given by:
(A)   \(x_p = x_{0p} + v_{p^t}, \text{with} \; x_{0p} = 0\)

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