Two trains $P$ and $Q$ are moving along parallel tracks with same uniform speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$. The driver of train $P$ decides to overtake train $Q$ and accelerates his train by $1 \mathrm{~m} \mathrm{~s}^{-2}$. After $50 \mathrm{~s}$, train $P$ crosses the…

Question

Two trains $P$ and $Q$ are moving along parallel tracks with same uniform speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$. The driver of train $P$ decides to overtake train $Q$ and accelerates his train by $1 \mathrm{~m} \mathrm{~s}^{-2}$. After $50 \mathrm{~s}$, train $P$ crosses the engine of train $Q$. Find out what was the distance between the two trains initially, provided the length of each train is $400 \mathrm{~m}$.

Aicharya · Accepted Answer

Let the initial distance between two trains be $x$. Distance travelled by train $P$ in $50 \mathrm{~s}$ :
$S_{P}=u t+\frac{1}{2} a t^{2}=20 \times 50+\frac{1}{2} \times 1 \times 50^{2}=2250 \mathrm{~m}$
Distance travelled by train $Q$ in $50 \mathrm{~s}$ :
$S_{Q}=u t=20 \times 50=1000 \mathrm{~m}$
Now $S_{P}-S_{Q}=2250-1000=1250 \mathrm{~m}$. This distance must be equal to the initial distance between the trains plus the sum of the lengths of the two trains.
$x+800=1250 \Rightarrow x=450 \mathrm{~m}$

Two trains \(P\) and \(Q\) are moving along parallel tracks with same uniform speed of \(20 \mathrm{~m}…

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