# An object with a mass of 3 kg is acted on by two forces. The first is F_1= < 2 N , 8 N> and the second is F_2 = < -1 N, -3 N>. What is the object's rate and direction of acceleration?

Jul 3, 2016

$a = \frac{\sqrt{26}}{3} \text{ } \frac{m}{s} ^ 2$

#### Explanation:

$1 - \text{Find the composition of the two vectors}$

${F}_{1} = < 2 , 8 > \text{ ; } {\vec{F}}_{1} = < 2 i + 8 j$
${F}_{2} = < - 1 , - 3 > \text{ ; } {\vec{F}}_{2} = - i - 3 j$
${\vec{F}}_{R} : \text{composition of the two vectors}$
${\vec{F}}_{R} = \left(2 - 1\right) i + \left(8 - 3\right) j \text{ ; } {\vec{F}}_{R} = i + 5 j$

$2 - \text{Find the magnitude of } {F}_{R}$
$| | {F}_{R} | | = \sqrt{{1}^{2} + {5}^{2}} = \sqrt{1 + 25} = \sqrt{26}$

$3 - \text{Find acceleration of this object using Newton's second law}$

$a = \frac{| | {F}_{R} | |}{m}$

$a : \text{represents acceleration of the object}$
$m : \text{represents mass of the object}$

$a = \frac{\sqrt{26}}{3} \text{ } \frac{m}{s} ^ 2$

$4 - \text{The direction of object moving is being shown in the animation}$