Physics

Problem

For a locomotive of mass

2.0\times10^{5}\,\text{kg}

hauling a train on level track, the mechanical power output of the engine varies with its speed according to

P = k v

, where

k = 4.0\times10^{5}\,\text{W\,s\,m}^{-1}

. No other horizontal forces act on the locomotive–train system. a. (i) Express the horizontal tractive force exerted by the wheels on the track in terms of

k

and

v

. b. (ii) Form the differential equation linking the acceleration of the train to its speed and hence obtain a formula for the speed

v(t)

when the train starts from rest at

t = 0

. c. (iii) Calculate the speed after

60\,\text{s}

. d. (iv) Determine the distance travelled in the first

60\,\text{s}

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