A person is running at his maximum speed of 4m/s to catch a train. When he is 6m from the door of the compartment the train starts to leave the station at a constant acceleration of 1m/s2. Find how long it takes him to catch up the train.

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A person is running at his maximum speed of 4m/s to catch a train. When he is 6m from the door of the compartment the train starts to leave the station at a constant acceleration of 1m/s². Find how long it takes him to catch up the train.

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Detailed Solution

The initial speed of man, u_m= 4 m/s

u_relative= 4 m/s

Relative acceleration, a_rel= -1 m/s²

s=6m

t=?

s= ut+(1/2)at²

$6 = 4 t + \frac{1}{2} \times - 1 \times t^{2}$

$12 = 8 t - t^{2}$

$t^{2} - 8 t + 12 = 0$

$t^{2} - 6 t - 2 t + 12 = 0$

$t (t - 6) - 2 (t - 6) = 0$

t=2 sec or 6 sec

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