# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < -5 N , 8 N> and the second is F_2 = < -2 N, 3 N>. What is the object's rate and direction of acceleration?

Oct 20, 2016

$| \overline{A} | = \frac{\sqrt{170}}{4} \frac{m}{s} ^ 2$
$\theta \approx 4.7$radians measured counterclockwise from the positive x axis.

#### Explanation:

$\overline{F} = {F}_{1} + {F}_{2}$

$\overline{F} = < - 7 N , 11 N >$

Using $\overline{F} = m \overline{A}$:

$\overline{A} = < - \frac{7}{4} \frac{m}{s} ^ 2 , \frac{11}{4} \frac{m}{s} ^ 2 >$

The acceleration is:

$| \overline{A} | = \sqrt{{\left(\frac{7}{4}\right)}^{2} + {\left(\frac{11}{4}\right)}^{2}} \frac{m}{s} ^ 2$

$| \overline{A} | = \frac{\sqrt{170}}{4} \frac{m}{s} ^ 2$

Correct the angle for the 4th quadrant:

$\theta = {\tan}^{-} 1 \left(\frac{11}{-} 7\right) + 2 \pi$

$\theta \approx 4.7$radians measured counterclockwise from the positive x axis.