1. 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 break at the yellow light. This results in an uniform deceleration.
The distance between the two light is ‘x’.
If the speed of the train would be 20% faster at the yellow light, what must be the minimum distance between the two lights. The deceleration does not change.
How to solve:
From the equations of motion we select v² = u² + 2as
In the case of the speed = 100%, 0 = u² + 2ax ⇒ x = u²/2a
In the case of the speed = 120%, 0 = (1.2u)² + 2ax ⇒ x = (1.44u²)/2a
Ratio of distance in case one to distance in case two is 1 to 1.44 therefore the distance new distance must be 1.44x