A motorcycle has a maximum power of 72 kilowatts. The motorcycle and its rider a

Question

A motorcycle has a maximum power of 72 kilowatts. The motorcycle and its rider are travelling along a straight horizontal road. When they are moving at a speed of V ms^-
1 , they experience a total resistance force of magnitude kV newtons, where k is a constant. (a) The maximum speed of the motorcycle and its rider is 60ms^-
1 . Show that k = 20 (b) When the motorcycle is travelling at 20ms^-
1 , the rider allows the motorcycle to freewheel so that the only horizontal force acting is the resistance force. When the motorcycle has been freewheeling for t seconds, its speed is vms^-
1 and the magnitude of the resistance force is 20v newtons. The mass of the motorcycle and its rider is 500 kg. (i) Show that dv/dt= -
v/25 (ii) Hence find the time that it takes for the speed of the motorcycle to reduce from 20ms
^-1 to 10ms^-
1 .

Explanation / Answer

force=kV power=kV*V=k*V^2 k*V^2=72*1000 as V=60, k=72000/3600=20 b)force=-20*v(as it is the resistance force,opposes motion) mass*acceleration=-20*v 500*dv/dt=-20*v so dv/dt=-v/25 (ii)dv/dt=-v/25 dv/v=-dt/25 ln(v)=-t/25 ln(20)-ln(10)=-t/25 so t=17.3287 sec

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