# 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 = < -2 N, 3 N>. What is the object's rate and direction of acceleration?

Jan 4, 2017

The acceleration is $= 2.15 m {s}^{- 2}$ at $144.5$º

#### Explanation:

The resultant force is

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

vecF=〈-5,2〉+〈-2,3〉=〈-7,5〉

The magnitude of $\vec{F}$, is =∥vecF∥=∥〈-7,5〉∥

$= \sqrt{49 + 25} = \sqrt{74}$

The rate of acceleration is =(∥vecF∥)/m=sqrt74/4=2.15ms^(-2)

The direction is $= \arctan \left(- \frac{5}{7}\right) = 144.5$º