Question

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?

Answer 1

The rate of acceleration is `1.25 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((3/4)^2+1^2) = 5/4 m/(sec^2) = 1.25 m/sec^2`