$.$A $100-$g bullet is fired from a rifle having a barrel $0\mathrm{.}600$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 $15000110000$x$225000$x$2,$ 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$)$ What If$?$ If the barrel is $1\mathrm{.}00$ m long, how much work is done, and $($c$)$ how does this value compare with the work cal culated in part $($a$)?$ W