# An object with a mass of 9 kg is acted on by two forces. The first is F_1= < -3 N , 8 N> and the second is F_2 = < 6 N, -3 N>. What is the objects rate and direction of acceleration?

Acceleration $a = \frac{\sqrt{34}}{9} = 0.6478835439 \text{ } \frac{m}{\sec} ^ 2$
directed $\theta = {59}^{\circ} 2 ' 10.48 ' '$

#### Explanation:

Adding the forces ${F}_{1}$ and ${F}_{2}$

$F = \sqrt{{\left(6 - 3\right)}^{2} + {\left(8 - 3\right)}^{2}}$

$F = \sqrt{9 + 25}$

$F = \sqrt{34}$

Acceleration $a = \frac{\sum F}{m} = \frac{\sqrt{34}}{9} = 0.6478835439 \text{ } \frac{m}{\sec} ^ 2$

Direction $\theta = {\tan}^{-} 1 \frac{8 - 3}{6 - 3} = {59}^{\circ} 2 ' 10.48 ' '$

God bless....I hope the explanation is useful.