The modern statement of Newton’s Second Law states…

The acceleration of an object is directly proportional to the force acting on the object, and inversely proportional to the mass of the object.

You can see, then, that Newton’s Second Law tells us how forces and accelerations are related to each other.

Mathematically, we write this as…

\(\color{black}{\vec{a} = \frac{\Sigma \vec{F}}{m}}\)


This should make some sense to you. If you push on two identical objects with different forces, the larger force will provide the larger acceleration. Likewise, if you push with the same force on two different objects, the larger object will experience less acceleration.

With a little bit of algebraic rearrangement, we write this as a vector equation.

\(\color{black}{\Sigma \vec{F} = m \vec{a}}\)


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