The graph shows a force in the x $-$direction $F_x$ acting on an object as a function of position $x$ of the object. Find the work done for each of the following intervals.

a$)$ from $x=0m$ to $x=3\mathrm{.}0m,$

b$)$ from $x=4\mathrm{.}0m$ to $x=7\mathrm{.}0m,$

c$)$ from $x=7\mathrm{.}0m$ to $x=10m.$

d$)$ If the object was moving with a velocity of $2\mathrm{.}0$ m$/$s at $x=0,$ find its velocity at $x=3\mathrm{.}0m.$