# A jeep chases a thief with a constant velocity #v#. When the jeep is at distance d from the thief, he starts to run with a constant acceleration #a#. Show that the police will be able to catch the thief when #v >= sqrt(2ad)#?

##### 1 Answer

Shown

#### Explanation:

Given is speed of police jeep

Distance between the thief and the police jeep

At this point constant acceleration of thief

Let the time when both meet

Let

Using kinematic expression

we get

During this time interval distance traveled by police jeep

Which is also

Equating two we get

From (1) and (2) we get

Solving quadratic for

For a real time