First slide

Rectilinear Motion

Question

Two objects moving along the same straight line are leaving point A with an acceleration a,2a and velocity 2u, u respectively at time t=0. The distance moved by the
object with respect to point A when one object overtakes the other is

Moderate

A

$\frac{3 u^{2}}{a}$
B

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

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

$\frac{6 u^{2}}{a}$

Solution

Let both will meet at point B
$x = 2 u t + \frac{1}{2} a t^{2} \Rightarrow x = u t + \frac{1}{2} (2 a) t^{2}$
$\begin{array}{l} So 2 u t + \frac{1}{2} a t^{2} = u t + a t^{2} \\ u t = \frac{1}{2} a t^{2} \Rightarrow t = \frac{2 u}{a} \\ So x = 2 u (\frac{2 u}{a}) + \frac{1}{2} a {(\frac{2 u}{a})}^{2} = \frac{6 u^{2}}{a} \end{array}$

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