The engineer of a train moving at a speed v1 sights a good train at a distance d ahead of him on the same track moving in the same direction with speed v2. He puts the brakes and gives his train a constant retardation a. There will be no collision if:-

a) d ≥ [(v1 - v2)^2]÷2a

b) d ≤ [(v1- v2)^2]÷2a

c) d = [(v1 - v2)^2]÷2a

d) d > [(v1 - v2)^2] ÷2a

Asked by acv27joy | 22nd Sep, 2018, 02:13: PM

Expert Answer:

The train which is moving with speed v1 should stop completely before reaching the second train
which is moving with speed v2.
relative speed of first train with respect to the second train = (v1-v2)
retardation a, distance d and relative velocity are related by the equation of motion " v2 = u2 -2aS ", where v is final velocity which is zero in this case, u is initial velocity, a is retardation and S is distance travelled.
hence with the given information, we get the condition for stopping of first train when it just reaches the second train as given below
(V1-V2)2 = 2×a×d   or the distance d = (V1-V2)2 / (2×a)
to avoid collision, d > (V1-V2)2 /(2×a)

Answered by Thiyagarajan K | 24th Sep, 2018, 12:07: AM

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