### Video Transcript

If a body of mass one kilograms moves under the action of forces ๐น sub one equals ๐ plus eight ๐ minus five ๐ newtons and ๐น sub two equals two ๐ minus seven ๐ plus eight ๐ newtons, what is its acceleration?

Weโll refer to the mass of our body one kilogram as ๐. And weโre told the two forces ๐น one and ๐น two that are acting on the body. We want to solve for the bodyโs resultant acceleration. Weโll call that ๐. To solve for ๐, letโs start by recalling Newtonโs second law of motion.

Newtonโs second law tells us that the net force that acts on an object is equal to that objectโs mass times its acceleration. So in our case, we can write ๐น one plus ๐น two equals ๐ times ๐ or ๐น one plus ๐น two all divided by ๐ equals ๐. Since weโre given ๐น one, ๐น two, and ๐ in our problem statement, we can plug in to solve for the acceleration.

In the numerator of our fraction, we have our two forces ๐น one and ๐น two being added together. When we combine them taking care to separate them out by ๐, ๐, and ๐ components, they result in three ๐ plus ๐ plus three ๐ newtons. Thatโs the net force acting on our object.

And the mass of the object is one kilogram, which means that ๐ is equal to three ๐ plus ๐ plus three ๐ metres per second squared. Thatโs the acceleration of our object under the influence of these two forces.