Deriving F = ma from momentum and acceleration measurements

Step 1 of 4: Defining momentum and force

Intuition

Momentum measures 'amount of motion' — a slow truck and a fast bullet can carry the same momentum. Force is what makes this 'amount of motion' grow or shrink.

\vec{p} = m\vec{v}, \qquad \vec{F} \equiv \frac{d\vec{p}}{dt}

Analysis

Newton stated his second law in the general form: force is the rate of change of 'quantity of motion' $\vec{p} = m\vec{v}$ . This form remains correct when mass varies (a rocket expelling gas) and is the version that survives in relativistic mechanics.