Q: Two trains one travelling at 54 kmph and the other at 72 kmph are headed towards one another along a straight track. When they are 1/2 km apart, both derives simultaneously see the other train and apply their brakes. If each train is decelerated at the rate of 1 m-s2, will there be a collision ?
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Sol: Velocity of the first train is 54 kmph = 15 m/s Distance travelled by the first train before coming to rest
$\large S_1 = \frac{u^2}{2a} = \frac{225}{2 \times 1} $
S1 = 112.5 m
Velocity of the second train is 72 kmph = 20 m/s
Distance travelled by the second train before coming to rest
$\large S_2 = \frac{u^2}{2a} = \frac{400}{2 \times 1} $
S2 = 200 m
Total distance travelled by the two trains before coming to rest
S = S1 + S2
= 112.5 + 200 = 312.5 m
Because the greater than 312.5 m, there will be no collision between the two trains.