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

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

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

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

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

answer is D.

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Detailed Solution

Let both will meet at point B.

x = 2ut + $\frac{1}{2} {at}^{2} \Rightarrow x = ut + \frac{1}{2} (2 a) t^{2}$

So $2ut + \frac{1}{2} {at}^{2} = ut + {at}^{2}$

$ut = \frac{1}{2} {at}^{2} \Rightarrow t = \frac{2 u}{a}$

So $x = 2 u (\frac{2 u}{a}) + \frac{1}{2} a {(\frac{2 u}{a})}^{2} = \frac{6 u^{2}}{a}$

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