A $50-$g bullet is fired from a rifle having a barrel $0\mathrm{.}540$ 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 $16000+10000x-24000x^2,$ 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. $($Enter your answer to at least two decimal places.$)$ kJ

$($b$)$ If the barrel is $0\mathrm{.}95$ m long, how much work is done? $($Enter your answer to at least two decimal places.$)$

kJ

$($c$)$ How does this value compare with the work calculated in part $($a$)?$

percent error $=\%$