# An object with a mass of 2 kg is acted on by two forces. The first is F_1= <4 N , 6 N> and the second is F_2 = < 1 N, 7 N>. What is the object's rate and direction of acceleration?

Dec 19, 2016

The answer is $= 6.96 m {s}^{- 2}$ and the direction is 69º

#### Explanation:

The combination of the 2 forces is

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

vecF=〈4,6〉+〈1,7〉=〈5,13〉

The magnitude of $\vec{F}$ is

∥vecF∥=∥〈5,13〉∥=sqrt(25+169)=sqrt194

The rate of acceleration is =(∥vecF∥)/m=sqrt194/2=6.96ms^(-2)

The direction of acceleration is

=arctan(13/5)=69º