# 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 = < 6 N, -3 N>. What is the objects rate and direction of acceleration?

Jul 6, 2016

$a = \frac{\sqrt{5}}{9} \text{ } \frac{m}{s} ^ 2$
$\text{Please look at the animation for direction of acceleration}$

#### Explanation: $\text{There are two force acting on body in different directions}$
$\text{First ,we have to find the vectorial sum of the two forces.}$

${F}_{1} = < - 7 , 1 > \text{ ; } {F}_{2} = < 6 , - 3 >$

${\vec{F}}_{1} = - 7 i + j \text{ ; } {\vec{F}}_{2} = 6 i - 3 j$

${\vec{F}}_{R} : \text{represents the vectorial sum of "vec F_1" and } {\vec{F}}_{2}$

${\vec{F}}_{R} = \left(- 7 + 6\right) i + \left(1 - 3\right) j$

${\vec{F}}_{R} = - i - 2 j$

$\text{now,we need to find the magnitude of } {\vec{F}}_{R}$

${F}_{\text{net"=sqrt((-1)^2+(-2)^2)=sqrt(1+4)=sqrt5" }} N$

$\text{We have to use the Newton's second law of motion :}$

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

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

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

$\text{direction of acceleration is being shown in animation above.}$