# An object with a mass of 2 kg is acted on by two forces. The first is F_1= < 8 N , 3 N> and the second is F_2 = < -7 N, 1 N>. What is the object's rate and direction of acceleration?

Dec 28, 2016

The acceleration is $= 2.06 m {s}^{- 2}$ at an angle of $76$º

#### Explanation:

The net force acting on the object is

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

vecF=〈8,3〉+〈-7,1〉=〈1,4〉

The magnitude of the force is ∥vecF∥=∥〈1,4〉∥

$= \sqrt{1 + 16} = \sqrt{17}$

The acceleration is =(∥vecF∥)/m=sqrt17/2=2.06 ms^(-2)

The direction is $\arctan \left(\frac{4}{1}\right) = 76$º