Question

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

• A. $225\text{m}$
• B. $375\text{m}$
• C. $450\text{m}$
• D. $700\text{m}$

Answer 1

The correct option is C $450\text{m}$

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