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.

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

Tardigrade Admin · Accepted Answer

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} \times 2 \times t^{2} = t^{2}

To get into the train, the distance traveled by the man is

x = x_{1} + 9 = t^{2} + 9 ... (i)

As the man covers the distance x with uniform speed in time t, we have

x = υ t ... (ii)

Substitutiong Eq.

(ii)

in

(i)

, we get

υ t = t^{2} + 9 \Rightarrow t^{2} - υ t + 9 + 0 \Rightarrow t = \frac{υ \pm υ ^{2} - 36}{2}

For real value of t, the discriminant of the above quadrati cequation should be greater than or equal to zero.

υ^{2} - 36 \geq 0 \Rightarrow υ^{2} \geq 36 \Rightarrow υ \geq 6

.
Therefore, the speed of the man to get into the train is

6 m s^{- 1} .

$4 m s^{- 1}$

$5 m s^{- 1}$

$6 m s^{- 1}$

$7 m s^{- 1}$

Q. 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 2ms−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.

4ms−1

5ms−1

6ms−1

7ms−1

$4 m s^{- 1}$

$5 m s^{- 1}$

$6 m s^{- 1}$

$7 m s^{- 1}$