Question

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.

Options

• 12.2 s

• 15.3 s

• 9 s

• 17.2 s

Answer 1

17.2 s

Explanation:

Given: u = 0, t = 5 sec, v = 108 km/hr = 30 m/s

By eqⁿ of motion v = u + at

or a = `v/t = 30/5` = 6 m/s²  .....[∵ u = 0]

S₁ = `1/2` at² = `1/2 xx 6 xx 5^2` = 75 m

Distance travelled in first 5 sec is 75 m.

Distance travelled with uniform speed of 30 m/s is S₂

395 = S₁ + S₂ + S₃

⇒ 395 = 75 + S₂ + 45

⇒ S₂ = 275 m

Time taken to travel 275 m = `275/30` = 9.2 sec

For retarding motion, we have

0² – 30² = 2(– a) × 45, we get a = 10 m/s²

S = `ut + 1/2` at²

⇒ 45 = `30t + 1/2 (-10)t^2`

⇒ 45 = 30t – 5t²

On solving we get, t = 3 sec

Total time taken = 5 + 9.2 + 3 = 17.2 sec.