# An object with a mass of 14 kg is acted on by two forces. The first is F_1= < 5 N , 3 N> and the second is F_2 = < 2 N, 7 N>. What is the object's rate and direction of acceleration?

May 22, 2016

The acceleration will be $0.87$ $m {s}^{-} 2$ at ${55}^{o}$ to the positive x-axis.

#### Explanation:

First find the magnitude of the force acting, which is the vector sum of the forces:

$F = \sqrt{{\left(5 + 2\right)}^{2} + {\left(3 + 7\right)}^{2}} = = \sqrt{{7}^{2} + {10}^{2}} = \sqrt{49 + 100}$
$= \sqrt{149} \approx 12.2$ $N$

Then, using Newton's Second Law:

$a = \frac{F}{m} = \frac{12.2}{14} \approx 0.87$ $m {s}^{-} 2$

To find the direction:

$\tan \theta = \text{opposite"/"adjacent} = \frac{10}{7}$

Which yields $\theta = {55}^{o}$