An engine of power 1.5 MW applies a force for 6 minutes on a train moving with a velocity of 10 `ms^(-1)`. If there is no friction and the velocity attained is 25 `ms^(-1)`, find the mass of the train.

Explanation

Power = 1.5 MW `= 1.5 xx 10^(6)` W , Time = 6 min `= 6 xx 60 = 360` sec. , Initial velocity : u = 10 m/s
Final velocity v = 25 m/s , Mass of the train = m
Power `= (w)/(t) = ((1)/(2) mv^(2) - (1)/(2) m u^(2))/(t) = 1.5 xx 10^(6) = ((1)/(2) m [25^(2) - 10^(2)])/(360)`
`m = (1.5 xx 10^(6) xx 2 xx 360)/(625 - 100) = 2.05 xx 10^(6)` kg