# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < -1 N , 3 N> and the second is F_2 = < 6 N, 5 N>. What is the object's rate and direction of acceleration?

Jun 3, 2017

The rate of acceleration is $= 2.36 m {s}^{-} 2$ in the direction of =58º anticlockwise from the x-axis

#### Explanation:

The resultant force is

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

$= < - 1 , 3 > + < 6 , 5 >$

$= < 5 , 8 >$

We apply Newton's second Law

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

Mass, $m = 4 k g$

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

$= \frac{1}{4} < 5 , 8 > = < \frac{5}{4} , 2 >$

The magnitude of the acceleration is

$| | \vec{a} | | = | | < \frac{5}{4} , 2 > | |$

$= \sqrt{{\left(\frac{5}{4}\right)}^{2} + {\left(2\right)}^{2}}$

$= \sqrt{5.5625} = 2.36 m {s}^{-} 2$

The direction is $\theta = \arctan \left(\frac{8}{5}\right)$

The angle lies in the 1st quadrant

theta=arctan(8/5)=58º anticlockwise from the x-axis