The engine of a locomotive exerts a constant force of 8.0 105 N to accelerate a train to 82 km/h. Determine the time (in min) taken for the train of mass 1.7 107 kg to reach this speed from rest. min

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

Explanation:

Hi there!

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 * 10⁵ N / 1.7 * 10⁷ kg = a

a = 4.7 * 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 * 10⁻² m/s² · t

t = 23 m/s / 4.7 * 10⁻² m/s²

t = 4.9 * 10² s

Let's convert the seconds into minutes:

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

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