A locomotive with a (constant) power capability of 3.0 MW can accelerate a train

Question

A locomotive with a (constant) power capability of 3.0 MW can accelerate a train from a speed of 9.9 m/s to 31 m/s in 4.8 min. (a) Calculate the mass of the train. Find (b) the speed of the train and (c) the force accelerating the train at 2.6 min after it started accelerating from the speed of 9.9 m/s. (d) Find the distance moved by the train during the 4.8 min interval that it took to reach the speed of 31 m/s. Note: This Problem involves constant power, not constant force.

Please explain and show steps , thank you!

Explanation / Answer

given,

power = 3 MW

initial velocity = 9.9 m/s

final velocity = 31 m/s

time = 4.8 min

energy = power * time

energy = 3 * 10^6 * 4.8 * 60

energy = 864000000 J

energy = change in kinetic energy

864000000 = 0.5 * m * vf^2 - 0.5 * m * vi^2

864000000 = 0.5 * m * 31^2 - 0.5 * m * 9.9^2

mass m = 2002340.7 kg

energy after 2.6 min

energy = 3 * 10^6 * 2.6 * 60

energy = 468000000 J

468000000 = 0.5 * 2002340.7 * v^2 - 0.5 * 2002340.7 * 9.9^2

v = 23.779 m/s

b) speed of train = 23.779 m/s

energy = force * velocity

468000000 = force * 23.779

force = 19681231.3386 N

d = Vin*t+(Vfin-Vin)*2/3*t

d = 9.9 * t + 21.1 * (2/3) * t

d = 9.9 * 4.8 * 60 + 21.1 * (2/3) * 4.8 * 60

d = 6902.4 m

distance travelled = 6902.4 m

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