# An object with a mass of 14 kg is acted on by two forces. The first is F_1= < 5 N , 6 N> and the second is F_2 = < -9 N, 4 N>. What is the object's rate and direction of acceleration?

##### 1 Answer
Jul 23, 2017

$\vec{a} = < - \frac{2}{7} , \frac{5}{7} >$

$| \vec{a} | = \frac{\sqrt{29}}{7} \frac{m}{s} ^ 2$

$\theta = {111.8}^{o}$

#### Explanation:

Let's find the sum of the forces :

$\vec{{F}_{1}} + \vec{{F}_{2}} = < 5 , 6 > + < - 9 , 4 > = < - 4 , 10 >$

Now from the ${2}^{\text{nd}} L a w o f N e w \to n :$

ΣvecF=mveca=>veca=(ΣvecF)/m=1/14*<-4,10> =

$< - \frac{2}{7} , \frac{5}{7} >$

So $\vec{a} = < - \frac{2}{7} , \frac{5}{7} >$

The magnitude is $| \vec{a} | = \sqrt{\frac{4}{49} + \frac{25}{49}} = \frac{\sqrt{29}}{7} \frac{m}{s} ^ 2$

The angle with the horizontal is $\theta = \arctan \left(\frac{\frac{5}{7}}{- \frac{2}{7}}\right) =$

$\arctan \left(- \frac{5}{2}\right) = {111.8}^{o}$