# Work(as function of time)

by Weave
Tags: function, time, workas
 P: 143 1. The problem statement, all variables and given/known data A body of mass m accelerates uniformly from rest to a speed $$v_{f}$$ in time $$t_{f}$$ Show that the work done on the body as a function of time, in terms of $$v_{f}$$,$$t_{f}$$ is: $$\frac{1}{2}m\frac{v_{f}^2}{t_{f}^2} t^2$$ 2. Relevant equations 1)$$W=\int F*dx$$ 2)$$V_{f}=at$$ 3)$$F=m\frac{V}{t}$$ 3. The attempt at a solution Well I know I would start out integrating equation 1 with equation 3. Then what?
 P: 143 Ah of course I get it now: $$r=\frac{1}{2}at^2$$ $$W=F*r \longrightarrow \frac{1}{2}ma^2t^2 \longrightarrow \frac{1}{2}m\frac{v^2}{t_{f}^2}t^2$$