Question

A student is standing at a distance of 50 metres from the bus. As soon as the bus starts its motion with an acceleration of $1{\text{m/s}}^2$ , the student starts running towards the bus with an uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is

• A. $5\text{m/s}$
• B. $8\text{m/s}$
• C. $10\text{m/s}$
• D. $12\text{m/s}$

Answer 1

The correct option is C $10\text{m/s}$

Let the student will catch the bus after $t$ sec. So it will cover distance $ut$. Similarly, distance travelled by bus will be $\frac{1}{2}a{t}^2$ for the given condition
$ut=50+\frac{1}{2}a{t}^2$
$u=\frac{50}{t}+\frac{t}{2}$ (As $a=1{\text{m/s}}^2$)
To find the minimum value of $u,\frac{du}{dt}=0,$
$0=-\frac{50}{t^2}+\frac{1}{2}\Rightarrow t^2=100$
$t=10\text{sec}$
Then, $u=\frac{50}{10}+\frac{10}{2}=10\text{m/s}$