# How do you find done in moving a particle P (1, 3) to Q(-3, 5) if the magnitude and direction of the force is given by v=-2i+3j?

Jan 10, 2017

$W D = 14 J$

#### Explanation:

Word done $= \vec{F} . \vec{s}$

displacement in this case is given by $\vec{P Q}$

$\vec{P Q} = \vec{q} - \vec{p} = \left(\begin{matrix}- 3 \\ 5\end{matrix}\right) - \left(\begin{matrix}1 \\ 3\end{matrix}\right) = \left(\begin{matrix}- 4 \\ 2\end{matrix}\right)$

$W D = \vec{F} . \vec{P Q} = \left(\begin{matrix}- 2 \\ 3\end{matrix}\right) . \left(\begin{matrix}- 4 \\ 2\end{matrix}\right) = \left(- 4\right) \times \left(- 2\right) + 3 \times 2$

$W D = 8 + 6 = 14 J$