# 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 = < 2 N, 6 N>. What is the object's rate and direction of acceleration?

$F = {F}_{1} + {F}_{2} = < 2 N , 6 N > + < 3 N , - 4 N > = < 5 N , 2 N >$
So, the resultant force has a magnitude of $\sqrt{{5}^{2} + {2}^{2}} N = \sqrt{29} N$
So the magnitude of the acceleration is as $\frac{\sqrt{29}}{4} m {s}^{-} 2$
And the direction is given as : $\tan \theta = \frac{2}{5}$ where $\theta$ is the angle the direction makes with the positive x-axis.