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A man running with a uniform speed ‘u’ on a straight road observes a stationary bus at a distance ‘d’ ahead of him. At that instant, the bus starts with an acceleration ‘a’. The condition that he would be able to catch the bus is__?

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d \leq \frac{u^{2}}{a}

d \leq \frac{u^{2}}{2 a}

d \leq \frac{u^{2}}{3 a}

d \leq \frac{u^{2}}{4 a}

answer is B.

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Detailed Solution

The condition that he would be able to catch the bus is

d \leq \frac{u^{2}}{2 a}

Let them meet at time t. At that time, the velocity of man will be greater or equal to that of bus.
Distance travelled will be time, t

S_{1} = ut

and

S_{2} = \frac{1}{2} a t^{2}

.
The final separation must be small or equal to the initial distance, ‘d’.
Since, the bus is stationary with respect to man, so,

T_{\min} = \frac{u}{a}

d \leq u (u / a) - \frac{1}{2} a (\frac{u^{2}}{a^{2}}) = \frac{u^{2}}{2 a}

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