- #1

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## Homework Statement

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}

## Homework Equations

P = Fv

F = ma

## The Attempt at a Solution

(i)

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 = kv

^{2}, 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.

Thanks