Question

At time $t=0$, two bodies A and B are at the same point. A moves with constant velocity $V$ and B starts from rest and moves with constant acceleration. Relative velocity of B with respect to A when the bodies meet each other is:

• A. $\frac{V}{2}$
• B. $\frac{V}{3}$
• C. $V$
• D. $2V$

Answer 1

The correct option is C $V$

Let the final relative velocity of B wrt A, when it crosses A, be: $v^{\prime }$.

It is given initial relative velocity of B wrt A is: $0-V=-V$

Initial relative displacement and final relative displacement is $0$ as the particles are at the same position initially and finally. Hence, total relative displacement of B wrt A is $0$.

From third equation of motion,

$v_f^2=v_i^2+2as$

$v^{\prime 2}=V^2$

$v^{\prime }=\pm V$

As seen before, $-V$ corresponds to the initial relative velocity.

Hence, $+V$ corresponds to final relative velocity.