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  4. 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

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Q. 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 isPhysics Question Image

Motion in a Straight Line

Solution:

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