Question

A subway train starts from rest and accelerate at 2m/s^2 for 10sec and then goes at constant speed for30sec and then decelerate at 4m/s^2 till rest, find the distance between stations.

Answer 1

see the above images.....

Answer 2

case 1 :- train starts from rest and accelerate at 2m/s² for 10sec.
then, distance covered in 10sec , S
S = ut + 1/2 at² [ from formula]
= 0.t + 1/2 × 2 × 10² [ initial velocity, u = 0]
= 100m

velocity after 10sec , v = u + at
v = 0 + 2 × 10 = 20 m/s

case2:- trains moves with constant speed 20m/s for 30sec.
so, distance covered in 30sec , S'
S' = vt = 20 × 30 = 600m

case3: - train decelerates at 4m/s² till rest.
initial velocity, u = 20m/s in this case.
deceleration , a = -4 m/s²
v² = u² + 2aS" [ from formula]
0 = (20)² + 2(-4)S"
400 = 8S" => S" = 50m

so, total distance covered by train = S + S' + S"
= 100 + 600 + 50 = 750m