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

Explanation:

During the first 5 seconds, the metro train goes from rest to 108 km/h (30 m/s). The acceleration is calculated using the equation:

v = u + at 30 = 0 + a × 5 a = 6 m/s²

The distance travelled during this phase is:

d₁ = ut + 1/2 × a × t² = 0 × 5 + 1/2 × 6 × 5² = 75 m

The train moves with constant velocity of 30 m/s for a certain distance. The remaining distance after the accelerating and decelerating phases is:

395 - 75 - 45 = 275 m

The time taken during this phase is:

t₂ = d / v = 275 / 30 = 9.17 seconds

Finally, the train comes to rest after travelling 45 m with uniform retardation. Using the equation for retardation:

v² = u² + 2ad 0 = 30² + 2 × a × 45 a = -10 m/s²

The time taken to stop is:

v = u + at 0 = 30 + (-10) × t₃ t₃ = 3 seconds

The total time of travel is the sum of the three phases:

t₁ + t₂ + t₃ = 5 + 9.17 + 3 = 17.17 seconds

The correct answer is d) 17.2s.