An object with a mass of 2 kg is acted on by two forces. The first is F_1= <5 N , 6 N> and the second is F_2 = < 1 N, -4 N>. What is the object's rate and direction of acceleration?

Dec 27, 2016

The answer is $= 3.16 m {s}^{- 2}$ at 18.4º

Explanation:

The net force is

$= \vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

vecF=〈1,-4〉+〈5,6〉=〈6,2〉

The magnitude of vecF=∥〈6,2〉∥=sqrt(36+4)=sqrt40

As, $F = m \cdot a$

$a = \frac{F}{m} = \frac{\sqrt{40}}{2} = 2 \frac{\sqrt{10}}{20} = \sqrt{10} = 3.16 m {s}^{- 2}$

The direction is

$\tan \theta = \frac{2}{6} = \frac{1}{3}$

theta=18.4º