First slide

Rectilinear Motion

Question

Two trains, which are moving along different tracks in opposite directions, 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 function of time as the trains slow down. The separation between the trains when both have stopped is

Moderate

A

120 m
B

280 m
C

60 m
D

20 m

Solution

Initial distance between trains is 300 m. Displacements of trains can be calculated by area under V-t graph.
$\begin{array}{l} Displacement of train 1 = \frac{1}{2} \times 10 \times 40 = 200 m \\ Displacement of train 2 = \frac{1}{2} \times 8 \times (- 20) = - 80 m \end{array}$
$which means it moves towards left .$
$∴ Distance between the two is 300 - 200 - 80 = 20 m .$

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