Motion physics?

Question

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

Answer 1

For postion 1

Initial velocty u1 =0

Calculate the acceleration

v1=u1+at1

a = (v1-u1)/t1=((108*5/18)-0)/5

   =6 m/s^2

Calculate the distance travelled in 5 sec

s1=uti+(1/2)at1^2

   =0+(1/2)(6)(5)^2

   =75 m

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For postion 2

s2=395-75-45=275 m

Calculate the time

t2=245/30=9.1667

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For postion 3

v=u-at3

0=30-at3

a =30/t3

s3=ut3-(1/2)at3^2

45=30t3-(1/2)(30/t3)t3^2--->45=30t3-15t3

t3=3 s

Calculate the total time

t=5+9.1667+3=17.1667 s