14. A train 500 m long is moving on a straight track with a speed of 80.0 km/h.

Question

14. A train 500 m long is moving on a straight track with a speed of 80.0 km/h. The engineer applies the brakes 2.0 s after the front end of the train goes through the crossing. Later the back end passes the crossing with a speed of18.0 km/h. Disregard the width of the crossing. Assume constant acceleration. (a) Express both speeds in m/s. (4 points) (b) Determine acceleration of the train. (4 points) (b) Calculate how long the train blocked the crossing. (4 points) (c) If the train maintains the same acceleration, what distance will the front end travel after it passes the crossing until it stops? (4 points)

Explanation / Answer

d = 500m
v = 80 km/h
t = 2s
u = 18 km/h

a)
v = 80 kmph = 22.22 m/s

u = 18 kmph = 5 m/s

b)
v^2 = u^2 + 2as

(5^2) - (22.22^2) = 1000a  

=> a = -0.469 m/s^2 (or -0.5 m/s^2 rounded off)

c)
t = v-u/a
=> t = (5 - 22.22)/-0.469
= 36.7 secs (or 37 s rounded off)

d)
v^2 = u^2 + 2as
v = 0
=> -u^2 = 2as
=> -(22.22)^2 = -0.469(2)s
=> s = 526.4 m

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