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

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

Then,

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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