The given question is incomplete. The complete question is as follows.
A 75-g bullet is fired from a rifle having a barrel 0.540 m long. Choose the origin to be at the location where the bullet begins to move. Then the force (in newtons) exerted by the expanding gas on the bullet is [tex]14,000 + 10,000x − 26,000x^{2}[/tex], where x is in meters. Determine the work done by the gas on the bullet as the bullet travels the length of the barrel.
Explanation:
We will calculate the work done as follows.
W = [tex]\int_{0}^{0.54} F dx[/tex]
= [tex]\int_{0}^{0.54} (14,000 + 10,000x - 26,000x^{2}) dx[/tex]
= [tex][14000x + 5000x^{2} - 8666.7x^{3}]^{0.54}_{0}[/tex]
= 7560 + 1458 - 1364.69
= 7653.31 J
or, = 7.65 kJ (as 1 kJ = 1000 J)
Thus, we can conclude that the work done by the gas on the bullet as the bullet travels the length of the barrel is 7.65 kJ.
