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

Jun 26, 2016

The rate of acceleration is $1.25 \frac{m}{\sec} ^ 2$
Directed along the vector
a = {3/4 m/(sec^2) ; 1 m/sec^2}

#### Explanation:

Let's add two vectors that represented these two forces:
F_1 + F_2 = {-2N+5N ; -6N+2N} = {3N ; -4N}

Now, applying the Second Newton's Law, acceleration is a vector with the following components:
a = {3/4 m/(sec^2) ; 4/4 m/sec^2} = {3/4 m/(sec^2) ; 1 m/sec^2}

The rate of acceleration is the length of this vector:
$| a | = \sqrt{{\left(\frac{3}{4}\right)}^{2} + {1}^{2}} = \frac{5}{4} \frac{m}{{\sec}^{2}} = 1.25 \frac{m}{\sec} ^ 2$