A metro train starts from rest and in 5 s achieves 108 ~km / h . After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.

Step-by-step solution

Given, v=108 ~km / h =30 ~m / s For first equation of motion v=u+a t 30=0+a 5 ( u=0) or a=6 ~m / s ^2 So, distance travelled by metro train in 5 s s₁= 1 2 a t^2= 1 2 (6) (5)^2=75 ~m Distance travelled before coming to rest =45 ~m So, from third equation of motion aligned & 0^2=(30)^2-2 a^ 45 & or a^ = 30 30 2 45 =10 ~m / s ^2 & aligned Time taken in travelling 45 m is t₃= 30 10 =3 ~s Now, total distance =395 ~m ie, 75+s^ +45=395 ~m or s^ =395-(75+45)=275 ~m t₂= 275 30 =9.2 ~s Hence, total time taken in whole journe