How Do You Calculate Work Done by a Variable Force Along a Displacement?

[Jacob87411]

A single conservative force acts on a 5.00 kg particle. The equation Fx = (2x + 4) N describes this force, where x is in meters. As the particle moves along the x-axis from x = 2.60 m to x = 6.20 m, calculate the following.
(a) the work done by this force
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Alright this seems pretty straight forward...W=FD, distance equals the change in X which is (6.2-2.6) which equals 3.6...The force acting on the particle is where I get a bit confused. F=2x+4...do you do it with x=6.2 or 2.6? Or do you find the value of 6.2 and subtract is from 2.6? Thanks for any help

 

[Fermat]

In the general case, you would do an integration.

WD = int, from x=2.6 to x=6.2, of Fx dx

However, in this particular case, since Fx is linear, then you can just take the average Force.

F_av = (F_6.2 + F_2.6)/2.

 

[Hootenanny]

The force is not constant. You need to integrate to find the work done.