The engine of a locomotive exerts a constant force of 8.1*10^5 n to accelerate a train to 68 km/h. determine the time (in min) taken for the train of mass 1.9*10^7 kg to reach this speed from rest.

443.1 s

Explanation:

Given

Engine of a locomotive exerts a force of

Mass of train

Final speed (v)

F=ma

so

and acceleration is

Explanation:

It is given that,

Force acting on the engine,

Initial speed of the engine, u = 0 (at rest)

Final speed of the engine, v = 68 km/h = 18.88 m/s

Mass of the train,

We need to find the time taken by the train. Firstly, we will find the acceleration of the engine from Newton's second law of motion as :

Now using first equation of motion to find time taken as :

t = 449.52 seconds

or

t = 7.49 minutes

So, the time taken for the train to reach this speed is 7.49 minutes. Hence, this is the required solution.