Finding work done on object with a chnaging force

[emilykorth]

Homework Statement

A single force acts on a 5.0 kg particle-like object in such a way that the position of the object as a function of time is given by x = 3.0t - 4.0t ^2 + 1.0t ^3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 2.0 s.

Homework Equations

W=Fd

The Attempt at a Solution

I started by finding the derivative of x = 3.0t - 4.0t ^2 + 1.0t ^3 which would be the velovity of the particle like object. (v=3-8t+3t^2)Then I plugged in 0 for when time=0 to find the velocity and then plugged in 2 for t to find the velocity when t=2 seconds. I then used the equation W=.5m(v^2-vo^2) to find that W=20 Joules however this was wrong
What am I doing wrong?

 

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