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  4. 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? <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-cfdjxxeozadct0im.jpg /> <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-cfdjxxeozadc2dgq.jpg />

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Q. 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?
Question Question

NTA AbhyasNTA Abhyas 2022

Solution:

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
$\left(\text{s}\right)_{\text{relative}}=s_{1}-s_{2}=\left(200\right)-\left(- 80\right)=280$
Final separation $=300-280=20\,m$