A car of mass 500 kg has a maximum speed of 40 ms-1 on a level road with the engine of the car working at a constant power of 20 kW. The resistance to motion is proportional to the square of the speed.
(i) find its acceleration when the speed is 20 ms-1
(ii) find the distance traveled while the speed increases from 20 ms-1 to 30 ms-1
(iii) when the car reaches the speed of 30 ms-1, the power is switched off. Find the time required to reduce the speed from 30 ms-1 to 20 ms-1
P = Fv
F = ma
The Attempt at a Solution
F = P/v = 20000/20 = 1000 N
a = F/m = 1000/500 = 2 ms-2
For (ii) and (iii), I don't know...
the resistance = kv2, how to find the value of k? and how to continue after that? I think kinematics doesn't work because the acceleration is not constant.