Car Chase
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/s2.
(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:
Position of the car:
xc = v0ct
Position of the police cruiser:
xp = v0pt
+ ½ at2
In order for us to find the distance traveled by the cars, which is
equal to their position at the time they meet, we must:
(a) set xp
= xc in the two equations and solve for t
(b) set xp = xc = x
and eliminate t between the two equations.