Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down th

Question

Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are $300 m$ apart. Graphs given below show their velocities as a function of time as the trains slow down. What is the separation between the trains (in metre) when both have stopped?

TestHub · Accepted Answer

Using the concept that the area under the v-t graph gives the change in displacement.

$s_{1} = \frac{1}{2} \times 10 \times 40 = 200 m$

$s_{2} = \frac{- 1}{2} \times 8 \times 20 = - 80 m$

Relative displacement

$s_{relative} = s_{1} - s_{2} = (200) - (- 80) = 280$

$F i n a l s e p a r a t i o n = 300 - 280 = 20 m$

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