Grade 11Mechanics

A train stopping at two stations d distance apart takes time t on the journey from one station to other. Assuming that its motion is first of uniform acceleration α and then immediately of uniform retardation β, show that 1/α+1/β=t*t/2d

Nirupam Nishant

9 Years agoGrade 11

1 Answer

Vikas TU

9 Years ago

In the question, it is not given that the movement of the train is of uniform velocity so we can assume that half is accelerated and half is retarded that is α = β

D = distance v₀ = maximum velocity

Distance travelled = Area under v-t graph

d = ½ v₀t

v₀= 2d/t

As we know that

v₀²/ 2α + v₀²/2 β = d

4d^2/2xt*t*α + 4d^2/2**t*t* β = d

2d/t*t* α + 2d/ t*t* β = 1

1/ α + 1/ β = t*t /2d

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A train stopping at two stations d distance apart takes time t on the journey from one station to other. Assuming that its motion is first of uniform acceleration α and then immediately of uniform retardation β, show that 1/α+1/β=t*t/2d

Nirupam Nishant

1 Answer

Vikas TU

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