A car traveling at a constant speed of 45.0m/s passes a trooper hidden behind a billboard. One second after th

Question

A car traveling at a constant speed of 45.0m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out in pursuit to catch it. The trooper accelerates at 3.00m/s^2 from rest. How long will it take the trooper to overtake the car?

Answer 1

The car's position from when the trooper Begin's pursuit will be will be
x(t)=45*(t+1)

and the trooper's position will be
x(t)=.5*3*t^2
When the two are at the same position, x(t) will be the same.
.5*3*t^2-45*(t+1)=0
t^2-30*t-30=0
Take the positive root at 31 seconds.

Note: The existence of a negative root can be explained. Since I arbitrarily chose t=0 to be the time that the trooper started from rest, the time from t>=0 is linear. The linear equations however describe what would have happened if the motion were linear with t<0. The negative root is at t=-.97 seconds. This would be where the two would have passed if the trooper followed the same motion in negative time. t=0 is the min of a parabola.

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