Problem 2-101 - Linear Kinematics - Part 7 - (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
\(x_p = x_{0p} + v_{0p} + ½ \;at^2\)

Part (a), \(\text{displacement} \; = 2.9 \times 10^2\; m\)

Correct!

In fact all three methods will give the correct (and same) answer.
 

(a)
\(x_c = v_{0c^t} = 290 = 18t \\ t = 16\; s\)
 
(b)

\(x_p = v_{0p^t} + ½ \;at^2 = 290 = 0 + ½ (2.2)(t^2) \\ t^2 = 2(290)/(2.2) = 264 \\ t = 16\; s\)
 
(c)

\(x_p = x_c \\ v_{0c^t} = ½ \;at^2 \\ t = 2(v_{0c})/a = 2(18)/(2.2) = 16 \;s\)

These are all the answer to part (b).

 

You have completed this problem.