The Chase Problem - Application of equations of motion

This is a short, application of equations of motion. The problem statement and the approach to solution is discussed.
A police inspector in a jeep is chasing a pickpocket in a straight line. The jeep has a maximum uniform speed v. the pickpocket rides on a motor cycle of a waiting friend when the jeep is at a distance d away, and motor cycle starts with constant acceleration a. What should be the speed of police to caught pickpocket?

Imagine that the pickpocket is caught at a time t after motor cycle starts. The distance travelled by the motor cycle during this interval is 

During this time t, the jeep will travel a distance, 

From these two equations, by equating S, we will get


The pickpocket will be caught if t is real and positive. This will be possible if 

That is, if the speed of police jeep is greater than or equal to √2ad, the pickpocket will be caught at a time, t.
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