A.2.19—Newton’s second law forms

Constant mass

For a body of constant mass, Newton’s second law becomes

$$\vec F_{net}=m\vec a$$

Use the resultant force, not one arbitrarily selected force.

General momentum form

The broader statement is

$$\vec F_{net}=\frac{\Delta\vec p}{\Delta t}$$

or its instantaneous form. This is the safer form when mass changes or when momentum is the quantity given.

Check what changes

If mass is constant, $\Delta p=m\Delta v$, so the two forms agree. If mass enters or leaves the system, include the momentum carried by that mass and define the system carefully.

Common trap

Do not double the acceleration simply because an applied force doubles when a fixed resistive force remains; calculate the new resultant force first.