# An object with a mass of 9 kg is acted on by two forces. The first is F_1= << -7 N , 1 N >> and the second is F_2 = << 4 N, -3 N >>. What is the objects rate and direction of acceleration?

Jun 8, 2017

The rate of acceleration is $= 0.4 m {s}^{-} 1$ in the direction of =213.7º anticlockwise from the x-axis

#### Explanation:

The resultant force is

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

$= < - 7 , 1 > + < 4 , - 3 >$

$= < - 3 , - 2 >$

We apply Newton's second Law

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

Mass, $m = 9 k g$

$\vec{a} = \frac{1}{m} \cdot \vec{F}$

$= \frac{1}{9} < - 3 , - 2 > = < - \frac{1}{3} , - \frac{2}{9} >$

The magnitude of the acceleration is

$| | \vec{a} | | = | | < - \frac{1}{3} , - \frac{2}{9} > | |$

$= \sqrt{{\left(- \frac{1}{3}\right)}^{2} + {\left(- \frac{2}{9}\right)}^{2}}$

$= \sqrt{0.16049} = 0.4 m {s}^{-} 2$

The direction is $\theta = \arctan \left(\frac{2}{3}\right)$

The angle lies in the 3rd quadrant

theta=arctan(2/3)=180+33.7º=213.7º anticlockwise from the x-axis