# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < 6 N , -2 N> and the second is F_2 = < -5 N, 3 N>. What is the object's rate and direction of acceleration?

Dec 7, 2016

$0.354$ $\frac{m}{s} ^ 2$ at an angle of ${45}^{o}$ to $x$-axis

#### Explanation:

As ${F}_{1} = < 6 N , - 2 N >$ and ${F}_{2} = < - 5 N , 3 N >$,

net force is ${F}_{1} + {F}_{2} = < 6 N - 5 N , - 2 N + 3 N >$

or $< 1 N .1 N >$

as the two components of net force are equal,

its direction will be ${45}^{o}$ to $x$-axis and

quantum is $\sqrt{{1}^{2} + {1}^{2}} = \sqrt{2} N$

and acceleration is $\frac{\sqrt{2}}{4}$ $\frac{m}{s} ^ 2$ or $\frac{1.4142}{4}$ $\frac{m}{s} ^ 2$

i.e. $0.354$ $\frac{m}{s} ^ 2$