Question

two trains are travelling with 120km/h and v km/h . length of train a is 100m and other is 200m resp. in 2 sec the second train overtakes the first . what is the velocity of second train?

Answer 1

Total distance travelled by the second train = (100+200)m=300m=0.3 km

Velocity of the first train = 120 km/h
​Velocity of the second train = v km/h

​So, relative velocity of the second train w.r.t. the first train $=\left\{\begin{array}{l}\mathrm{v}-120,\mathrm{if}\mathrm{the}2\mathrm{trains}\mathrm{are}\mathrm{running}\mathrm{parallel}\mathrm{to}\mathrm{each}\mathrm{other}(\mathrm{they}\mathrm{are}\mathrm{running}\mathrm{in}\mathrm{the}\mathrm{same}\mathrm{direction})\\ \mathrm{v}+120,\mathrm{if}\mathrm{the}2\mathrm{trains}\mathrm{are}\mathrm{running}\mathrm{anti}-\mathrm{parallel}\mathrm{to}\mathrm{each}\mathrm{other}(\mathrm{they}\mathrm{are}\mathrm{running}\mathrm{in}\mathrm{opposite}\mathrm{direction})\end{array}\right.$

Now, we know that:-

Distance=Speed x Time

$\Rightarrow 0.3=\left(v+120\right)\frac{2}{3600},or,0.3=\left(v-120\right)\frac{2}{3600}$

$\Rightarrow v+120=540,or,v-120=540$

$\Rightarrow v=420km/h,or,v=660km/h$

Thus, the velocity of the second train is 420 km/h if the trains are running in opposite direction, and 660 km/h if they are running in the same direction.