# An object with a mass of 5 kg is acted on by two forces. The first is F_1= <10 N , 6 N> and the second is F_2 = <4 N, 16 N>. What is the objects rate and direction of acceleration?

Feb 17, 2018

The rate of acceleration is $= 5.21 m {s}^{-} 2$ in the derection $= {57.5}^{\circ} \text{in the direction anticlockwise from the x- axis}$

#### Explanation:

The resultant force is

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

$= < 10 , 6 > + < 4 , 16 >$

$= < 14 , 22 > N$

The mass of the object is $m = 5 k g$

According to Newton's Second Law

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

Therefore,

The acceleration is

$\vec{a} = \frac{\vec{F}}{m} = \frac{1}{5} \cdot < 14 , 22 \ge < \frac{14}{5} , \frac{22}{5} >$

The rate of acceleration is

$| | \vec{a} | | = | | < \frac{14}{5} , \frac{22}{5} > | |$

$= \sqrt{{\left(\frac{14}{5}\right)}^{2} + {\left(\frac{22}{5}\right)}^{2}}$

$= 5.21 m {s}^{-} 2$

The direction is

$\theta = \arctan \left(\frac{22}{14}\right) = {57.5}^{\circ} \text{in the direction anticlockwise from the x- axis}$