A train starts from a station P with a uniform acceleration a1, for some distance and then goes with uniform retardation a2 for some more distance to come to rest at the station Q. The distance between the stations P and Q is 4Km and the train takes 4 minutes to complete this journey, then 1/a11/a2=

There are two case in given question:

1. When train moves with uniform acceleration

2. When train moves with uniform retardation.

 

For the 1st case,

Let the train start from a station P with uniform accleration a₁, with initial velocity u₁ and t₁ be the time when it reaches at some distance s₁

From kinematic eqution of motion we have,

v₁=u₁+a₁t₁         (u₁=0 Initialy at rest)

v₁=a₁t_{1     ....} (i)

For the 2nd case the final velocity of first interval will be intial velocity of second.

Let a₂ be uniform retardation, t₂ be the time when it travels a distance s₂ and comes to rest .

From kinematic equation of motion we have,

v₂ = u₂ - a₂t₂ = v₁ - a₂t₂    (v₂ = 0 finaly comes at rest)

v₁ = a₂t_{2  ... (iii)} 

 

Using kinematic equation of motion,