Question

A student is standing at a distance of 50 metres from a bus. As soon as the bus begins its motion (starts moving away from student) with an acceleration of 1 m s${}^{-2}$, 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 student is able to catch the bus is:

• A. $5m{s}^{-1}$
• B. $8m{s}^{-1}$
• C. $10m{s}^{-1}$
• D. $12m{s}^{-1}$

Answer 1

The correct option is C $10m{s}^{-1}$

$50+x=ut$ .....(1)
and $x=\frac{t^2}{2}$ ...(2)

From (1) and (2),
$50+\frac{t^2}{2}=ut\Rightarrow t^2-2ut+100=0$
For real roots, discriminant = 0
$\Rightarrow 4u^2-400=0\Rightarrow u=10m/s$