Question

A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of $1m/s^{-2}$, 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 $10m{s}^{-1}$

Let student will catch the bus after t sec. So it will cover distance ut.

Similarly distance travelled by the bus will be $\frac{1}{2}a{t}^2$ for the given condition.

$ut=50+\frac{1}{2}a{t}^2=50+\frac{t^2}{2}[a=1m/s^2]$

$\Rightarrow u=\frac{50}{t}+\frac{t}{2}$
To find the minimum value of u.
$\frac{du}{dt}=0,sowegett=10sec,$ then u = 10 m/s