A car ($m=540\,\text{kg}$) engine, has a power of $60\,\text{kW}$. The static friction coefficient between wheels and road is $k=0.6$. How long does it take to reach the speed of $27.7\,\text{m/s}$, with constant acceleration?
I have tried the following:
The energy to reach given speed is: $$\frac{mv^2}{2}=\frac{540\cdot 27.7^2}{2}=2.07\cdot 10^5\,\text{J}$$
In the meanwhile I dissipated (because of friction): $$-F_a\cdot s=-mgk\cdot\frac{1}{2}at^2=-mgk\cdot\frac{1}{2}\frac{\Delta v}{t}t^2=158,922\cdot t$$
The engine can do a work of $60,000\,\text{J}$ per second, so the work done is $60,000\cdot t$
So, I can do: $$2.07\cdot 10^5\,\text{J}+158,922\cdot t=60,000\cdot t$$ And I obtain a negative time. How is possible? What's wrong? Thanks a lot