Question #5476

the driver of a train travelling at 30 ms^-1 applies the brakes as the train enters a station. The train slows down at the rate of 4 m/s^-2. The platform is 400m long.Will the train stop in time?

Expert's answer

Let's make following denotations:

V = 30 m/s;

a = 4 m/s^2;

L = 400m.

V = a*T ==> T = V/a = 30/4 = 7.5 s - time needed the train to stop.

S = V*T - (a*T^2)/2 = 30*7.5 - (4*7.5^2)/2 = 112.5 - stopping distance.

S < L, so the train will stop in time.

V = 30 m/s;

a = 4 m/s^2;

L = 400m.

V = a*T ==> T = V/a = 30/4 = 7.5 s - time needed the train to stop.

S = V*T - (a*T^2)/2 = 30*7.5 - (4*7.5^2)/2 = 112.5 - stopping distance.

S < L, so the train will stop in time.

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