Question

a 12-kg block is acted upon by two forces that are in opposite direction, one a 540 Newton and the other of 1260 N. Determine the acceleration produced. How is the direction of the acceleration related to the forces?

Answer 1

Let the first force of 540 N acts upon a block in the positive $x$-direction, and the second one - 1260 N acts in the opposite direction. Let's find the net force that acts upon the block:

$$F_{net}=F_1-F_2=540\ N-1260\ N=-720\ N.$$

The sign minus means that the net force that acts upon the block directed in the opposite direction.

Let's find the acceleration from the Newton's Second Law of Motion:

$$a=\dfrac{-F_{net}}{m}=\dfrac{-720\ N}{12\ kg}=-60\ \dfrac{m}{s^2}.$$

The sign minus means that the block accelerates under the action of the net force in the opposite direction (-$x$-direction).