Question $1$

The work$-$energy theorem is $($assuming usual meanings for quantities$)$

W$\_($net $)=\backslash$int$\_($vec$($r$)\_(0))^($vec$($r$)\_($f$))$ vec$($F$)\_($net $)*$dvec$($r$)=(1)/(2)$mv$\_($f$)^(2)-(1)/(2)$mv$\_(0)^(2)=\backslash$Delta K$.$ The work$-$energy theorem is a purely

mathematical consequence of Newton's second law and is derived from it$.$ In other words,

Newton's second law implies the work$-$energy theorem. For motion along one$-$dimension, for

example the x direction, this is $\backslash$int$\_($x$\_(0))^($x$\_($f$))$ F$\_($net $,$x$)$dx$=(1)/(2)$mv$\_($f$,$x$)^(2)-(1)/(2)$mv$\_(0,$x$)^(2).$

Which of the following are true statements? Assume the usual meanings for quantities.

If vec$($F$)\_($net $)=$mvec$($a$)$ is true, then so is W$\_($net $)=\backslash$int$\_($vec$($r$)\_(0))^($vec$($r$)\_($f$))$ vec$($F$)\_($net $)*$dvec$($r$)=(1)/(2)$mv$\_($f$)^(2)-(1)/(2)$mv$\_(0)^(2)=\backslash$Delta K

Work is a vector quantity because it has a magnitude and can either be positive or negative.

A negative net work always implies a decrease of the object's kinetic energy.