Question

A man on the railway platform is just 9 m behind the entrance door of a train, when the train begins to move with a uniform acceleration of $2 \,m\, s^{-1}$ starting from rest. The man immediately picks up a uniform speed to get into the train and he just boards the train. Find the speed he picks up.

• A. $4 \,m\, s^{-1}$
• B. $5 \,m\, s^{-1}$
• C. $6 \,m\, s^{-1}$
• D. $7 \,m\, s^{-1}$

Answer 1

Answer: (C)

Let the speed of man be v and time taken by him to just get into the train be t. The distance traveled by train in time t is given by
$x_{1} = 0\times t+\frac{1}{2}\times2\times t^{2} = t^{2}$
To get into the train, the distance traveled by the man is
$x = x_{1} + 9= t^{2} +9 \quad ...\left(i\right)$
As the man covers the distance x with uniform speed in time t, we have
$x = \upsilon t\quad ...\left(ii\right)$
Substitutiong Eq. $\left(ii\right)$ in $\left(i\right)$, we get
$\upsilon t = t^{2} + 9 \Rightarrow t^{2} -\upsilon t +9 +0 \Rightarrow t = \frac{\upsilon \pm \sqrt{\upsilon ^{2}-36}}{2}$
For real value of t, the discriminant of the above quadrati cequation should be greater than or equal to zero.
$\sqrt{\upsilon ^{2}-36} \ge 0 \Rightarrow \upsilon ^{2} \ge 36 \Rightarrow \upsilon \ge 6$.
Therefore, the speed of the man to get into the train is $6 \,m\, s^{-1}.$