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Q.

Two objects are moving along the same straight line. They cross a point A with an acceleration $a a n d 2 a$ and velocity $2 u a n d u$ at time $t = 0$ . The distance moved by the object when one overtakes the other is

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a

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

b

$\frac{8 u^{2}}{a}$

c

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

d

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

answer is A.

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Detailed Solution

At the time of overtaking.

$s_{1} = s_{2} . 2 u t + \frac{1}{2} a t^{2} T h e r e f o r e, 2 u t + \frac{1}{2} a t^{2} = u t + \frac{1}{2} (2 a) t^{2} t \Rightarrow t = \frac{2 u}{a} T h e r e f o r e, s_{1} = s_{2} = (2 u) (\frac{2 u}{a}) + \frac{1}{2} (a) {(\frac{2 u}{a})}^{2} = \frac{6 u^{2}}{a}$

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