Question

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

• A. 5 ms^–1
• B. 8 ms^–1
• C. 10 ms^–1
• D. 12 ms^–1

Answer 1

Answer: (C)

10 ms^–1

Answer 2

Let student will catch the bus after $t$sec. So it will cover distance ut. Similarly distance travelled by the bus will be $\frac{1}{2}at^{2}$ for the given condition

$ut = 50 + \frac{1}{2}at^{2} = 50 + \frac{t^{2}}{2}$

⇒$u = \frac{50}{t} + \frac{t}{2}$ (As $a = 1m/s^{2}$)

To find the minimum value of u, $\frac{du}{dt} = 0$,

so we get t = 10 sec then u = 10 m/s.