# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < -3 N , 6 N> and the second is F_2 = < 7 N, -8 N>. What is the object's rate and direction of acceleration?

Aug 13, 2016

$\theta = \arctan \left(- \frac{1}{2}\right)$

$\left\mid \vec{a} \right\mid = \frac{\sqrt{5}}{2} \text{m/} {s}^{2}$

#### Explanation:

$\Sigma \vec{F} = m \vec{a}$

$\implies \left(\begin{matrix}- 3 \\ 6\end{matrix}\right) + \left(\begin{matrix}7 \\ - 8\end{matrix}\right) = 4 \left(\begin{matrix}{a}_{x} \\ {a}_{y}\end{matrix}\right)$

$\left(\begin{matrix}4 \\ - 2\end{matrix}\right) = 4 \left(\begin{matrix}{a}_{x} \\ {a}_{y}\end{matrix}\right)$

$\left(\begin{matrix}{a}_{x} \\ {a}_{y}\end{matrix}\right) = \left(\begin{matrix}1 \\ - \frac{1}{2}\end{matrix}\right)$

direction $\tan \theta = \frac{{a}_{y}}{{a}_{x}} = \frac{- \frac{1}{2}}{1}$, $\theta = \arctan \left(- \frac{1}{2}\right)$

$\left\mid \vec{a} \right\mid = \sqrt{{1}^{2} + {\left(- \frac{1}{2}\right)}^{2}} = \frac{\sqrt{5}}{2} \text{m/} {s}^{2}$