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

Jan 10, 2017

The acceleration is 〈-1,5/4〉ms^-2 in the direction $= - 51.3$º

#### Explanation:

The resultant force is

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

vecF=〈-5,2〉+〈1,3〉=〈-4,5〉

Applying Newton's second Law

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

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

=1/4*〈-4,5〉=〈-4/4,5/4〉=〈-1,5/4〉ms^-2

The direction is $= \arctan \left(\frac{5}{4} \cdot \frac{1}{-} 1\right) = \arctan \left(- \frac{5}{4}\right) = - 51.3$º