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

Question

A train is approaching the station with a velocity of 15 m/s. The engineer knows from experience that at this speed the brakes must be applied 1 km 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

1) a)

v^2=u^2+2as

0 = 15^2 + 2a*1000

-225 = 2a

a = -225 / 2000

acceleration = -0.1125 m/s^2

b) v = u+ at

0 = 15 + 0.1125 *t

t = 133.33 seconds

c) no, he won't be able to stop at the present acceleration

  v^2 - u^2 = 2aS

  S = -u^2 / 2a = - 30^2/2*-0.1125

= 4000 metres

he should apply the brakes before 4000 metres

v = u+at

0 = 30+0.1125 * t

t = 30/0.1125

=266.67 seconds,

,time taken = 266.67 seconds

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