# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < -4 N , 2 N> and the second is F_2 = < 2 N, -8 N>. What is the object's rate and direction of acceleration?

Jan 13, 2017

The acceleration is =〈-1/2,-3/2〉ms^-2 in the direction $251.6$º

#### Explanation:

The resultant force acting on the object is

$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

vecF=〈-4,2〉+〈2,-8〉=〈-2,-6〉

By Newton`s secod Law

$\vec{F} = m \cdot \vec{a}$

veca=vecF/m=1/4*〈-2,-6〉=〈-2/4,-6/4〉

veca=〈-1/2,-3/2〉

The acceleration is =〈-1/2,-3/2〉ms^-2

The direction is =180º+arctan((-3/2)/(-1/2))

=180º+arctan3=180+71.6=251.6º