First slide

Relative motion based problems

Question

Two particles A and B are initially at rest at the origin. They simultaneously start moving along positive x-axis, ‘A’ with constant velocity u and B with constant acceleration ‘a’. Then find the separation between the particles when their relative velocity is zero.

Moderate

A

$\frac{u^{2}}{4 a}$
B

$\frac{u^{2}}{2 a}$
C

$\frac{u^{2}}{a}$
D

$\frac{2 u^{2}}{a}$

Solution

Relative velocity at time t, $V_{r} = (u - at)$
Initially acceleration, $a_{r} = - a$
Using $V_{r}^{2} = u_{r}^{2} + 2 a_{r} x_{r},$
$\begin{array}{l} O = u_{}^{2} + 2 (- a) . x_{r} \\ \Rightarrow x_{r} = \frac{u^{2}}{2 a} \end{array}$

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