In order that a train can stop safely, it will always pass a signal showing a yellow light before it reaches a signal showing a red light.

Question 26

In order that a train can stop safely, it will always pass a signal showing a yellow light before it reaches a signal showing a red light. Drivers apply the brake at the yellow light and this results in a uniform deceleration to stop exactly at the red light.

The distance between the red and yellow lights is x.

If the speed of the train is increased by 20%, without changing the deceleration of the train, what must be the minimum distance between the lights?

A 1.20 x                       B 1.25 x                       C 1.44 x                      D 1.56 x

Reference: Past Exam Paper – November 2010 Paper 11 Q9 & November 2016 Paper 12 Q10

Solution:

Answer: C.

Since there is a uniform deceleration, we can use the equations of uniformly accelerated motion.

When the initial speed of train is u,

Distance between red and yellow lights = x

Final speed of train = v = 0     [the train stops]

v² = u² +2as

0 = u² + 2ax

u² ∝ x              [The distance is proportional to the square of the initial speed.]

Now, the initial speed of the train is increase by 20%.

New speed u_new = 100% + 20% = 120%

New speed u_new = 1.20 u

Since the deceleration is kept constant, u² ∝ x

New distance x_new ∝ (u_new)² = (1.20 u)² =  1.44 u² = 1.44 x                [since u² ∝ x]