Simple work and variable position question

[iJamJL]

Homework Statement

A one-dimensional force acts on a particle of mass m = 6.26 kg in such a way that its position is given by:

x = 0.484t^3 - 33.6t

Find W, the work done by this force during the first 1.49 s.

Homework Equations

W=F*s
W=mgs
Integration

The Attempt at a Solution

I just wanted to know whether I'm solving this correctly because I only have one more chance to input an answer in my online homework system (as those of you who have been helping me probably know by now.

Anyhow, this is what I've done.

W=Fs
F=mg
W=mgs
**Because the position is variable but the mass and gravity are constant, we integrate the formula given, and we get:

W=mg*∫x.dx= (.121t^4) - 16.8(t^2), from 0s to 1.49s

We come to:

W=mg*(-36.7)
W=6.26*9.81*(-36.7)= (-2253.8) J

Did I do this properly?

 

[ehild]

The problem does not say that the particle is subjected to gravity. F=ma, and the acceleration is second derivative of position. Find the force from the given x(t) function.

ehild