The Calculation of Time Taken for a Train to Reach a Speed of 82 km/h

The Engine of a Locomotive Exerts a Constant Force

The engine of a locomotive exerts a constant force of 8.0 x 10^5 N to accelerate a train to 82 km/h. We need to determine the time taken for the train, with a mass of 1.7 x 10^7 kg, to reach this speed from rest.

Calculation

Using Newton´s second law, we can calculate the acceleration of the train:

F = m · a

Where:

F = force exerted by the locomotive.

m = mass of the train.

a = acceleration of the train.

Solving the equation for the acceleration:

F/m = a

8.0 x 10^5 N / 1.7 x 10^7 kg = a

a = 4.7 x 10^-2 m/s²

Let´s convert 82 km/h to m/s:

82 km/h · (1000 m / 1 km) · (1 h /3600 s) = 23 m/s

Using the equation of velocity, we can calculate the time it takes for the train to reach a velocity of 23 m/s:

v = v0 + a · t

Where:

v = velocity at time t.

v0 = initial velocity (in this case, v0 = 0 because the train starts from rest).

a = acceleration.

t = time.

23 m/s = 0 +  4.7 x 10^-2 m/s² · t

t = 23 m/s /  4.7 x 10^-2 m/s²

t = 4.9 x 10² s

Let´s convert the seconds into minutes:

4.9 x 10² s · (1 min / 60 s) = 8.2 min

Answer

It will take the train 8.2 min to reach a speed of 82 km/h.

Explanation: Using Newton´s second law and the equations of motion, we calculated the acceleration, velocity, and time required for the train to reach the specified speed from rest.

The Calculation of Time Taken for a Train to Reach a Speed of 82 km/h

It will take the train 8.2 min to reach a speed of 82 km/h