First slide

Rectilinear Motion

Question

A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motorcycle. When he is at a distance x from the jeep, he accelerates from rest at a constant rate. Which of the following relations is true if the police is able to catch the dacoit?

Difficult

A

$v^{2} \leq α x$
B

$v^{2} \leq 2 α x$
C

$v^{2} \geq 2 α x$
D

$v^{2} \geq α x$

Solution

If police is able to catch the dacoit after time t, then
$\begin{array}{l} v t = x + \frac{1}{2} α t^{2} . This gives \frac{α}{2} t^{2} - v t + x = 0 \\ or t = \frac{v \pm \sqrt{v^{2} - 2 α x}}{α} \\ For t to be real, v^{2} \geq 2 a x \end{array}$

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