Work / Power done to a particle

1. Sep 27, 2009

Warmacblu

1. The problem statement, all variables and given/known data

A 1 kg particle starts from rest at x = 0 and moves under the influence of a single force Fx = 6.6 + 12.6x - 1.8x2, where Fx is in Newtons and x is in meters.

Find the work done by this force on the particle as the particle moves from x = 0 m to x = 1.5 m.

Find the power delivered to the particle when it is at x = 1.5 m.

2. Relevant equations

Integrals
V = (2K/m)1/2
P = Fv

3. The attempt at a solution

I solved the first part by solving the integral and plugging in 1.5. The answer was 22.05.

The second part I thought I had correct:

V = (2K/m)1/2, where K = W
V = (2(22.05)/1.5)1/2
V = 119.56 W

I tried variations on this number because I was certain I was correct, I even tried the negatives. Perhaps my equation for V is incorrect?

2. Sep 27, 2009

Staff: Mentor

m ≠ 1.5

3. Sep 27, 2009

Warmacblu

Wow, m equals mass?

V = (2K/m)1/2, where K = W
V = (2(22.05)/1)1/2
V = 6.64 m/s

W = 22.05 x 6.64

W = 146.43

4. Sep 27, 2009

Staff: Mentor

Uh, yeah... I hope you're not just plugging into formulas without knowing what they mean.

That formula for speed comes from the definition of kinetic energy, K = 1/2mv^2.

OK.
Why are you multiplying W by the speed? (And then calling it W!)

5. Sep 28, 2009

Warmacblu

I was just becoming very frustrated with this question because it seemed so easy but I guess I don't really understand the concepts yet.

I am trying to solve for power which is P - Fv. I solved for v and I guess I thought that my previous answer was the force but it wasn't, it was just the average power.

I believe that in order to solve this problem, I have to plug in 1.5 into the Fx equation given to solve for the force and multiply that by the velocity.

Note - I already used up all of my tries for this problem so I would just like to understand the concept of the question now.

6. Sep 28, 2009

Staff: Mentor

That's right. (In the future, try to take it slower. Double check each step.)

7. Sep 28, 2009

Warmacblu

Thanks, will do.