Starting from rest, a train travels with a constant acceleration of 2.0 m/s ^2 for half a minute. Subsequently, the brakes are applied, bringing the train to rest in one minute. Determine the total distance moved by the train in km.

Step-by-step solution

For the acceleration phase: Initial velocity, u = 0 Acceleration, a₁ = 2.0 m/s ^2 Time, t₁ = 0.5 min = 30 s Maximum velocity reached, v = u + a₁ t₁ = 0 + 2.0 30 = 60 m/s Distance covered during acceleration, s₁ = 1 2 a₁ t₁^2 = 1 2 2.0 (30)^2 = 900 m For the deceleration phase: Initial velocity, v = 60 m/s Final velocity, v_f = 0 Time, t₂ = 1 min = 60 s Distance covered during deceleration, s₂ = v + v_f 2 t₂ = 60 + 0 2 60 = 1800 m Total distance moved by the train, s = s₁ + s₂ = 900 + 1800 = 2700 m Converting to kil