A train starts from rest and moves with uniform acceleration a for some time and acquires a velocity v. It then moves with constant velocity for some time and then decelerates at a rate b and finally comes to rest at the next station if L is the distance between two stations then the total time of travel is
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2015-08-23T17:41:08+05:30

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U = 0
v = u + a t1  = a t1    =>    Time duration t1 = v / a
Distance travelled in time duration t1 = S1 = 1/2 a t1² ,   as u = 0
   S1 =  v² / (2 a)

The train moves with uniform velocity for duration  t2.
Distance travelled in time duration t2 = S2 = v * t2

acceleration rate = - b
Final velocity = 0          initial velocity = v
Time duration to stop = t3 = v / b
Distance travelled = S3 = v t3 - 1/2 b t3²  = v²/ (2 b)

Total distance travelled = S1 + S2 + S3 = L
     L = v²/ 2  (1/a  + 1/b) + v * t2
   t2 =   L/v - v/2 * [1/a + 1/b]

The total time duration = T = t1 + t2 + t3
       = v / a + L / v - v / 2 * [ 1 / a + 1 / b ] + v / b
       = L / v + v / 2 * [1/a  + 1/b]

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