Formula for Power from Kinetic Energy

Work Done = $$Fd$$

Power = $$Fv$$

If the (net) Work Done = Change in Kinetic Energy, and the object starts from rest:
Work Done = $$\frac{1}{2} mv^2$$

Power = $$\frac{1}{2} m av$$

Power = $$\frac{1}{2} F v$$

This isn't correct though. How do I remove factor of $$\frac{1}{2}$$?

1 Answer

It looks like you accidentally forgot the "power rule" in your third step.

Suppose that there is only kinetic energy and the object starts from rest.

Then $$W = \frac{1}{2} mv^2$$

Then, since power is $$P= \frac{dW}{dt}$$ we have that

$$P = \frac{dW}{dt} = \frac{1}{2} m \frac{d}{dt} v^2 = mv \dot{v} = (ma)v = F\cdot v$$