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

Q#26 (Past Exam Paper – November 2010 Paper 11 Q9 & November 2016 Paper 12 Q10
)


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?
1.20                       
1.25 x
1.44                      
1.56 x




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 unew = 100% + 20% = 120%

New speed unew = 1.20 u

Since the deceleration is kept constant, u2  x

New distance xnew  (unew)2 = (1.20 u)2 =  1.44 u2 = 1.44 x                

[since u2  x]

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