Question

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

• A. $d\le \frac{u^2}{a}$
• B. $d\le \frac{u^2}{2a}$
• C. $d\le \frac{u^2}{3a}$
• D. $d\le \frac{u^2}{4a}$

Answer 1

The correct option is B $d\le \frac{u^2}{2a}$

Let they will meet at time $t$. At that time, velocity of man must be greater or equal to as that of bus.

The distances travelled by the man and the bus in time $t$

$S_1=ut$ and $S_2=\frac{1}{2}a{t}^2$

For catching the bus by the man the final separation must be smaller than or equal to the initial separation $d$.

As, the bus is stationary with respect to man (initially). So,

$t_{min}=\frac{u}{a}$

This implies $d\le u\left(\frac{u}{a}\right)-\frac{1}{2}a\frac{u^2}{a^2}$ (That is, $t=\frac{u}{a}$)

$⟹d\le \frac{u^2}{2a}$