# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < 3 N , -4 N> and the second is F_2 = < 7 N, 6 N>. What is the object's rate and direction of acceleration?

Dec 25, 2016

The answer is $= 2.55 m {s}^{- 2}$ at 11.31º

#### Explanation:

The resultant force is
$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

vecF=〈3,-4〉+〈7,6〉=〈10,2〉

The magnitude of $\vec{F}$ is

=∥〈10,2〉∥

$= \sqrt{100 + 4} = \sqrt{104}$

The acceleration is $= \frac{F}{m} = \frac{\sqrt{104}}{4} = 2.55 m {s}^{- 2}$

The direction of acceleration is $= \arctan \left(\frac{2}{10}\right)$

=11.31º