Question

A person is at a distance x from a bus when the bus begins to move with a constant acceleration a. What is the minimum velocity , v , with which the person should run towards the bus so as to catch it ?

• A. $2ax$
• B. $\sqrt{2ax}$
• C. $ax$
• D. $\sqrt{ax}$

Answer 1

Answer: (B)

$\sqrt{2ax}$

Let us assume that the person catches with the bus in t seconds. So, in t seconds, the displacement of both person and the bus cover the same distance.

For bus, undergoing accelerated motion, displacement

$s=ut+0.5a{t}^2$

$s=0.5a{t}^2$

In time t, displacement of person who is moving with constant velocity is given by

s = vt

So, at the time of catching with the bus,

$vt=0.5a{t}^2+x$

$v=0.5at+x/t$

Since v is uniform velocity, dv/dt = 0

So we have, $0.5a-x/t^2=0\to t^2=x/0.5a\to t=\sqrt{x/0.5a}$

So, inserting this value of t again in v gives, v = $\sqrt{2ax}$