Question

A train start from rest and accelerates uniformly for 20 s to attain a velocity of 90km/h. It travels at constant velocity for 15minutes . the driver applies brakes to stop the train in next 5s . find the total displacement of the train.

Answer 1

Dear student,

Initial velocity (u) = 0 (started from rest)
final velocity (v) = 90km/h = 25m/s

From the equation
v = u + at (where a is acceleration & t is time)
Time taken to accelerate = 20sec
=> a= 5/4 m/s²
Displacement of the train during acceleration be s₁
s₁ =ut + 0.5xaxt² (u is initial velocity
a is acceleration
t is time
On putting values s₁ = 250m
Displacement during the constant velocity be s₂
s₂ =(velocity) x (time) (as acceleration is zero)
time of constant velocity = 15min = 15x60= 900sec
=>s₂ = 25 x 900 = 22500m
Displacement during retardation s₃
final velocity after braking = 0= v
Initial velocity = 25m/s
Time for braking = 5sec

use equation
v = u + at (u is initial velocity
a is retardation
t is time
a = -5m/s²
s₃ =ut + 0.5xaxt2
On putting values
s₃ = 187.5m
total displacement = s₁ +s₃+ s₂
= 22937.5m