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

Displacement of the car
$x_c = x_{0c} + v_{0c^t}$

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

Correct!

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