Newton's Second Law

When the forces do not cancel, the net force changes the motion: the object speeds up or slows down. How fast its speed changes, in m/s every second, is its acceleration $a$. Its unit is $\mathrm{m/s^2}$: an acceleration of $2\ \mathrm{m/s^2}$ means $2\ \mathrm{m/s}$ faster every second. Slowing down is an acceleration too, pointing backward. Newton's second law says how big it is:

$$\sum \vec{F} = m\vec{a}$$

The acceleration points the same way as the net force, and a larger mass gets less acceleration from the same force. Force is measured in newtons: $1\ \mathrm{N} = 1\ \mathrm{kg \cdot m/s^2}$.

N and mg cancel; the net force F minus f points right, and so does the acceleration.

Solve a problem in three steps: draw every force on the object, choose a positive direction, then write the net force as $\relax ma$.

A $5\ \mathrm{kg}$ crate is pushed right with $40\ \mathrm{N}$ while friction pulls left with $10\ \mathrm{N}$: $\relax 40 - 10 = 5a$, so $a = 6\ \mathrm{m/s^2}$ to the right.