Question

Two trains P and Q are moving along parallel tracks with the same uniform speed of 20 $m{s}^{-1}$. The driver of train P decides to overtake train Q and accelerates his train by 1 $m{s}^{-2}$. After 50 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 400m.

Answer 1

Let the initial distance between two trains be x.
Distance travelled by train P.in 50 s:
$S_p=ut+\left(1/2\right)a{t}^2$ = 20 $\times$ 50 + (1/2)$\times$ 1 $\times {50}^2$ = 2250m
Distance travelled by train Q in 50s:
$S_q=ut=20\times 50$ = 1000m
Now $S_p-S_q$ = 2250 - 1000 = 1250m. This distance must be equal to the initial distance between the trains plus the sum of the lengths of the two trains plus the sum of x + 800 = 1250 $\Rightarrow$ x = 450 m