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

Aug 12, 2017

$| \vec{a} | \approx 3.8 m \cdot {s}^{- 2}$

$\hat{a} = \frac{1}{\sqrt{58}} \left(7 \hat{i} - 3 \hat{j}\right)$

#### Explanation:

${\vec{F}}_{1} = \left(5 \hat{i} + \hat{j}\right) N$

${\vec{F}}_{2} = \left(2 \hat{i} - 4 \hat{j}\right) N$

${\vec{F}}_{n e t} = \left(7 \hat{i} - 3 \hat{j}\right) N$

$m = 2 k g$

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

$\vec{a} = \left(\frac{7}{2} \hat{i} - \frac{3}{2} \hat{j}\right) m \cdot {s}^{- 2}$

$| \vec{a} | = \sqrt{{\left(\frac{7}{2}\right)}^{2} + {\left(\frac{3}{2}\right)}^{2}}$

$\Rightarrow | \vec{a} | = \frac{\sqrt{58}}{2}$

$\Rightarrow | \vec{a} | \approx 3.80 m \cdot {s}^{- 2}$

$\vec{a} = | \vec{a} | \cdot \hat{a}$

$\hat{a} = \frac{\vec{a}}{|} \vec{a} |$

$\Rightarrow \hat{a} = \left(\frac{7}{2} \hat{i} - \frac{3}{2} \hat{j}\right) \cdot \frac{2}{\sqrt{58}}$

$\Rightarrow \hat{a} = \frac{1}{\sqrt{58}} \left(7 \hat{i} - 3 \hat{j}\right)$