A train is approaching the station with a velocity of 15m/n. The engineer knows

Question

A train is approaching the station with a velocity of 15m/n. The engineer knows from experience that at this speed the brakes must be applied 1km from the station in order to stop in time. Find the acceleration of the train as it stops. Determine the time it takes the train to stop. On another day the same train is approaching the station at 30^m/s. The engineer assumes that the brakes should be applied 2km away from the station. Will the train stop at the station? If not, determine how far away from the station the engineer should apply the brakes at this speed and how long (time) it takes the train to stop.

Explanation / Answer

(a) Speed of the tran = 15 m/s

Distance between the train and the station, when the engineer applies brake, d = 1 km = 1000 m

v^2 = u^2 + 2*a*d

=> 0 = 15^2 + 2*a*1000

=> a = -225/(2*1000) = -0.1125 m/s^2

(b) v= u + a*t

=> 0 = 15 - 0.1125*t

=> t = 15/0.1125 = 133.33 sec.

(c) Now the speed of the train = 30 m/s

and d = 2000 m

if a =  -0.1125 m/s^2

The the effective, d -

0 = 30^2 - 2*0.1125*d

=> d = 900 / (2*0.1125) = 4000 m

So, the train will stop at a distnce of 2 km after covering the station.

To stop the train exactly at the station, the engineer should apply the brake when the train is at a distance of 4 km from the station.

Consider the requisite time is t.

Then -

4000 = 30t - 0.5*0.1125*t^2

=> 0.05625*t^2 - 30t + 4000 = 0

So, t = {30 +/- sqrt[900 - 4*4000*.05625]} / (2*0.05625) = 266.67 sec.

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