# How do you find done in moving a particle P (0,0) to Q(4,7) if the magnitude and direction of the force is given by v=<1,4>?

Jun 6, 2018

$32 \text{ unit}$.

#### Explanation:

Suppose that, under the influence of a force $\vec{F} ,$ a particle

moves from point $P$ to point $Q$.

Then, the work $W$ done is given by, $W = \vec{F} \cdot \vec{P Q}$.

We have, $\vec{F} = \left(1 , 4\right)$ and for the displacement $\vec{P Q}$,

$\vec{P Q} = Q \left(4 , 7\right) - P \left(0 , 0\right) = \left(4 , 7\right)$.

$\therefore W = \left(1 , 4\right) \cdot \left(4 , 7\right) = \left(1\right) \left(4\right) + \left(4\right) \left(7\right) = 4 + 28 = 32 \text{ unit}$.