How do I solve for Work using only distance?

Question

Currently taking highschool physics when I came across this question in my homework:

"A basketball player is lifting weights. She benches 45 kg, moving it 0.5 meters. If she does this in 0.8 seconds, how much power does she use?"

I know how to find power, but I need to find work first, but I can't do that without being given force. My question is, given the values I have, how would I solve this?

I've been using W= F x d for finding work, and P= w/t for power.

Answer 1

Hi.

Here you need to first calculate the force so that you can then calculate the work done on the object.

F = ma

To get force, you need to know the acceleration of the object. To get that, you use the acceleration formula:

a = Δ v / Δ t = 0.5 m / 0.8 s = 0.625 m/s²

Now we can calculate the force:

F = ma = (45 kg) (0.625 m/s²) = 28.125 N

Now we can figure out the work done on the object.

W = Fd

W = 28.125 N x 0.5 m = 14.0625 N / m or 14.01625 J

Now we can calculate the power involved.

P = W / Δt = 14.01625 J / 0.8 s = 17.578125 W.

We need to adjust our answer to take account of significant figures. Since each of our variables has two significant figures, we'll round our answer to 17.58 W. That's our final answer.