Question

A 130 m long train was coming into a station. The train decelerated at a rate of 0.150 m/s2 as it entered the station. The station was 210 m long.

a) The driver managed to stop the train when the tail of the train reached the end of the station. What was the entering velocity of the train into the station? [2.5 marks]

b) If the driver wanted to stop the train at the middle of the station, what should be the rate of deceleration (consider entering velocity as that is calculated in question

‘a’)? [2.5 marks]

c) What was the time required to stop the train at the middle of the station? [2.5

marks]

d) If the train decelerates at a rate of 0.160 m/s2, where will the train stop (the

position of the nose of the train with respect to the end of the station)? [2.5 marks]

Answer 1

Given:

L = length of train = 130 m

D = length of station = 210 m

a = deacceleration rate = 0.15 m/s^2

a) When the tail of the train reached the end of the station, it stops.

Let the entering velocity be u.

final velocity = v = 0

distance traveled = s = 130 m

Applying the kinematic equation:

[answer]

b) If the driver wants to stop the train in the middle of the station, then let eh deacceleration rate be a'.

initial velocity = u = 6.24 m/s

final velocity = v = 0

distance travelled = 210/2 = 105 m

Applying the kinematic equation:

[answer]

c) Let the time required be t.

initial velocity = u = 6.24 m/s

final velocity = v = 0

a' = 0.185 m/s^2

Applying the kinematic equation:

v = u - a' t

0 = 6.24 - 0.185 *t

t = 6.24/0.185

= 33.73 s [answer]

d) Let the distance travelled be s.

initial velocity = u = 6.24 m/s

final velocity = v = 0

a = 0.16 m/s^2

Applying the kinematic equation:

The nose of the train stops at a distance 121.68 m from the end of the station. [answer]