# Video: Finding the Acceleration of a Body given the Force Vectors Acting on It

If a body of mass 1 kg moves under the action of forces ๐นโ = (๐ + 8๐ โ 5๐) N and ๐นโ = (2๐ โ 7๐ + 8๐) N, what is its acceleration?

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### Video Transcript

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

Weโll refer to the mass of our body one kilogram as ๐. And weโre told the two forces ๐น one and ๐น two that are acting on the body. We want to solve for the bodyโs resultant acceleration. Weโll call that ๐. To solve for ๐, letโs start by recalling Newtonโs second law of motion.

Newtonโs second law tells us that the net force that acts on an object is equal to that objectโs mass times its acceleration. So in our case, we can write ๐น one plus ๐น two equals ๐ times ๐ or ๐น one plus ๐น two all divided by ๐ equals ๐. Since weโre given ๐น one, ๐น 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 ๐น one and ๐น 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. Thatโs 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. Thatโs the acceleration of our object under the influence of these two forces.