Work done by expanding gas in a gun on a bullet

[TrippingBilly]

A 135 g bullet is fired from a rifle having a barrel 0.590 m long. Assuming the origin is placed where the bullet begins to move, the force (in Newtons) exerted by the expanding gas on the bullet is 20000 + 8000x - 22000x2, where x is in meters.

(a) Determine the work done by the gas on the bullet as the bullet travels the length of the barrel.
(b) If the barrel is 1.25 m long, how much work is done, and how does this value compare to the work calculated in part (a)?

For part A, i plugged in .590m into x for the equation of the force, multiplied that by .590 because W = Force x Distance, and since they wanted an answer in kJ i divided by 1000, but it says that my answer is incorrect. Any thoughts?

 

[Hootenanny]

Your answer would be correct if the force is uniform (constant),but since it isn't, some calculus is required. Note that the formal definition of work done by a force is;

W=\int^{x_{1}}_{x_{0}} F(x) \;dx

 

[TrippingBilly]

Wow, thanks. Never would have thought of that. Thanks to this forum for the first time ever I got a 100% on my physics homework
Thanks