The diagram shows an arrangement to stop trains that are travelling too fast. Trains coming from the left travel at a speed of 50 m s-1.

Question 36

The diagram shows an arrangement to stop trains that are travelling too fast.

Trains coming from the left travel at a speed of 50 m s^-1. At marker 1, the driver must apply the brakes so that the train decelerates uniformly in order to pass marker 2 at no more than 10 m s^-1.

The train carries a detector that notes the times when the train passes each marker and will apply an emergency brake if the time between passing marker 1 and marker 2 is less than 20 s.

How far from marker 2 should marker 1 be placed?

A 200 m                      B 400 m                      C 500 m                      D 600 m

Reference: Past Exam Paper – June 2013 Paper 12 Q7

Solution:

Answer: D.

Initial speed u = 50 m s^-1

Final speed (max) v = 10 m s^-1

Minimum time for passing between marker 1 and 2: t = 20 s

{If time is less than 20 s, it means that the train is moving too fast. So an emergency brake is then applied.}

Since the train undergoes uniform deceleration, we can use the equations of uniformly accelerated motion.

Distance between markers = s = ???

s = ut + ½ at²

To obtain the acceleration a:

a = (v-u) / t = (10 – 50) / 20 = - 2 m s^-2  

Replacing a in the equation,

s = ut + ½at²

s = (50×20) + (½×-2×20)²

s = 600 m