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

Apr 28, 2016

The resultant force acting is $< 5 , - 2 >$. The magnitude of the force is $5.4$ $N$, leading to an acceleration of $1.8$ $m {s}^{-} 2$ in a direction ${21}^{o}$ below the positive x axis.

#### Explanation:

First find the resultant force acting:

${F}_{1} + {F}_{2} = < - 2 + 7 , - 3 + 1 > = < 5 , - 2 >$

The magnitude of the force is:

$F = \sqrt{{5}^{2} + {\left(- 2\right)}^{2}} = \sqrt{25 + 4} \approx 5.4$ $N$

The magnitude of the acceleration is given by Newton's Second Law:

$a = \frac{F}{m} = \frac{5.4}{3} = 1.8$ $m {s}^{-} 2$

The direction of the acceleration will be given by:

${\tan}^{-} 1 \left(\frac{o p p}{a \mathrm{dj}}\right) = {\tan}^{-} 1 \left(- \frac{2}{5}\right) = - {21}^{o}$