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

Jan 27, 2017

The net acceleration is $= \sqrt{5} m {s}^{-} 2$ in the direction $= 63.4$º

#### Explanation:

The resultant force is

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

$\vec{F} = < - 2 , 5 > + < 4 , - 1 > = < 2 , 4 >$

We use Newton's secnd Law

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

$\vec{a} = \frac{\vec{F}}{m} = \frac{1}{2} \cdot < 2 , 4 > = < 1 , 2 >$

The net acceleration is $= | | \vec{a} | | = | | < 1 , 2 > | | = \sqrt{1 + 4} = \sqrt{5} m {s}^{-} 2$

The direction is $= \arctan \left(\frac{2}{1}\right) = 63.4$º