A 60-kg runner increases her speed from 2 m/s to 4.3 m/s in 5 s. Assuming she develops constant power during this time interval and neglecting air resistance, determine (a) the power developed, (b) the distance traveled.
P = W/t
T = kinetic energy = 1/2mv^2
The Attempt at a Solution
The power was easy:
T1 + U1->2 = T2
U1->2 = T2 - T1 = 1/2*m(v2^2 - v1^2) = 434.7 J
P = U/t = 434.7/5 = 86.9 W
Ok, but the displacement, I'm not sure:
P = W/t = Fd, and that's all I have. I don't know F. I know P, W,t, but without F or d, I'm slightly screwed. Can I have some help? If it helps, I DO know the answer, but I'd like to see a solution/arrive at an answer before looking at it.
I just tried Impulse-Momentum and STILL didn't get the right answer:
mv1 + Imp 1->2 = mv2
Imp 1->2 = F(t2-t1) and t2-t1 = 5s
F = (m(v2-v1))/(t2-t1) = 27.6
P = W/t = Fd/t -----> Pt/F = d
Using that, I'm getting the wrong answer of 15.74 m.