Question

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

• 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 the man meet the bus at time t.
Velocity of the man be u, acceleration of the bus be a, then
$ut=\frac{1}{2}a{t}^2+d$
For the time to be positive, the discriminant of the above expression should be greater than or equal to zero.
Required condition $d\le \frac{u^2}{2a}$