A bullet of 46 g is fired from a rifle having a barrel of 0.639 m long. Supposing the origin is positioned where the bullet starts to move, the force applied on the bullet by the expanding gas is F = a + b x - c x2, where a = 18800 N, b = 5090 N/m, c = 14300 N/m2, with x in meters.
Find out the work done by the gas on the bullet as the bullet travels the length of the barrel.