# An object with a mass of 5 kg is acted on by two forces. The first is F_1= < 1 N , 4 N> and the second is F_2 = < 2 N, -3 N>. What is the object's rate and direction of acceleration?

Jun 28, 2016

$a = \frac{\sqrt{10}}{5} \text{ } \frac{m}{s} ^ 2$

$\text{direction is shown in figure above.}$

#### Explanation:

$\text{given:}$

${F}_{1} = < 1 , 4 > \text{ ; } {\vec{F}}_{1} = i + 4 j$

${F}_{2} = < 2 , - 3 > \text{ ; } {\vec{F}}_{2} = 2 i - 3 j$

$\text{first let's find the resultant force :}$

${F}_{R} = \left(1 + 2\right) i + \left(4 - 3\right) j \text{ ; } {F}_{R} = 3 i + j$

$\text{now let's find the magnitude of resultant force :}$

${F}_{\text{net"=sqrt(3^2+1^2)=sqrt(9+1)=sqrt10" }} N$

$\text{And let's find acceleration using the newton's second law}$

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

$a : \text{represents acceleration of object}$
$m : \text{represents mass of object}$
${F}_{\text{net:""represents net force acting on object}}$

$a = \frac{\sqrt{10}}{5} \text{ } \frac{m}{s} ^ 2$

$\text{direction is shown in figure above.}$