Answer:
The answer is [tex]W=\frac{1}{2} m (v_2^{2} -v_1^{2} )[/tex]
Explanation:
Here you have to take into account the theorem of work and energy. This theorem says that the total work done by external forces on a body is used to modify the kinetic energy. So the only thing you have to do is determine the kinetic energy in the initial [tex](K_1)[/tex] and final moment [tex](K_2)[/tex], then the diference between them is the amount of net work that act over the body.
[tex]K_1=\frac{1}{2} m v_1^{2} [/tex]
[tex]K_2=\frac{1}{2} m v_2^{2} [/tex]
[tex]W=K_2-K_1=\frac{1}{2} m v_2^{2} - \frac{1}{2} m v_1^{2}=\frac{1}{2} m (v_2^{2} -v_1^{2} )[/tex]
