Force problem with equation Please see question. Need help with this problem.

[NasuSama]

Homework Statement

A one-dimensional force acts on a particle of mass m = 4.48 kg in such a way that its position is given by:

x = 0.221t^3 - 38.8t

Find W, the work done by this force during the first 1.41 s.

Homework Equations

W = F * d
F = ma

The Attempt at a Solution

dx/dt = v = 0.663t² - 38.8
dv/dt = a = 1.326t

At t = 1.41, we obtain approximately 1.87.

Then...

F = 4.48 * 1.87 ≈ 8.38

So...

W = 8.38 * (0.221 * (1.41)³ - 38.8(1.41))
≈ -453?

That answer is wrong.

 

[TSny]

Hello.

Are you familiar with the "work-energy theorem" that relates work to kinetic energy?

If not, you'll have to know how to use calculus to get the work done by a variable force.

 

[NasuSama]

Hello.

Are you familiar with the "work-energy theorem" that relates work to kinetic energy?

If not, you'll have to know how to use calculus to get the work done by a variable force.

Then, this means I need to use this form? W = ½ * m * v²?

Nevermind. You said I need to have the force expression .

 

[NasuSama]

Hold up.. I need to use this form!

W = ∫^(v = v_0,v_f) mv dv
= mv_f²/2 - mv_0²/2

 

[TSny]

Good.

 

[NasuSama]

Then, I need to determine the derivative of the displacement equation. Then, find v(0) and v(1.41) [The velocity at t = 0 AND the velocity at t = 1.41]. Finally, I find the work done, right?

This is what I have:

4.48/2 * ((-37.5)² - (-38.8)²) = -222

Am I on the right track?

 

[TSny]

Yes. (You already wrote the answer for the derivative of x in your first post.)