# An object with a mass of 9 kg is acted on by two forces. The first is F_1= < -1 N , 8 N> and the second is F_2 = < 6 N, -3 N>. What is the objects rate and direction of acceleration?

##### 1 Answer
Jun 21, 2016

$a = \frac{5 \sqrt{2}}{9} \text{ } \frac{m}{s} ^ 2$

#### Explanation:

${F}_{1} = < - 1 , 8 > \text{ ; } {F}_{2} = < 6 , - 3 >$

${F}_{1} = - i + 8 j \text{ ; } {F}_{2} = 6 i - 3 j$

${F}_{R} : \text{ Resultant Vector}$

${F}_{R} = \left(- 1 + 6\right) i + \left(8 - 3\right) j$

${F}_{R} = 5 i + 5 j$

$\text{the magnitude of "F_R" is "F_"net} = \sqrt{{5}^{2} + {5}^{2}}$

${F}_{\text{net}} = \sqrt{25 + 25}$

${F}_{\text{net"=5sqrt2" }} N$

$a : \text{acceleration of object , m=9 kg}$

$a = {F}_{\text{net}} / m$

$a = \frac{5 \sqrt{2}}{9} \text{ } \frac{m}{s} ^ 2$