\(\mathrm v=\mathrm u+\mathrm a\mathrm t,\; \) \(\mathrm s=\mathrm u\mathrm t+\frac12\mathrm a\mathrm t^2,\) \(\mathrm v^2=\mathrm u^2+2\mathrm a\mathrm s\)
\(\mathrm s=\;\) displacement, \(\mathrm t\) = time interval, \(\mathrm u=\) initial velocity, \(\mathrm v=\;\) final velocity, \(\mathrm a=\;\) acceleration
\(\mathrm a=\frac{\mathrm F}{\mathrm m}\)
\(\mathrm a=\;\) a= acceleration, \(\mathrm F=\) force, \(\mathrm m\;=\) mass
\(\mathrm W=\operatorname\Delta\mathrm E;\;\) where the applied force is in the same direction as the displacement, \(\mathrm W=\mathrm F\mathrm s,\;\)
\(\mathrm W\) = work, \(\;\mathrm F=\;\) force, \(\;\mathrm s=\) displacement, \(\operatorname\Delta\mathrm E=\;\) change in energy
\(\mathrm p=\mathrm m\mathrm v,\;\;\mathrm\Delta\mathrm p=\mathrm F\mathrm\Delta\mathrm t\)
\(\mathrm p\) = momentum, \(\mathrm v=\;\) velocity, \(\mathrm m\;=\) mass, \(\mathrm F\;\) = force, \(\triangle\mathrm p=\) change in momentum, \(\mathrm\Delta\mathrm t\) = time interval over which force \(\mathrm F\) acts
\({\mathrm E}_\mathrm k=\;\frac12\;\mathrm m\mathrm v^2\)
\({\mathrm E}_\mathrm k=\) kinetic energy, \(\;\mathrm m=\) mass, \(\mathrm v=\;\) speed
\(\operatorname\Delta{\mathrm E}_\mathrm p=\mathrm m\mathrm g\operatorname\Delta\mathrm h\)
\(\operatorname\Delta{\mathrm E}_\mathrm p=\;\) change in potential energy, \(\mathrm m=\;\) mass, \(\mathrm g\;=\;\) g = acceleration due to gravity, \(\triangle\mathrm h=\) change in vertical distance
\(\mathrm\Sigma\mathrm m{\mathrm v}_{\mathrm b\mathrm e\mathrm f\mathrm o\mathrm r\mathrm e}=\;\mathrm\Sigma\mathrm m{\mathrm v}_{\mathrm a\mathrm f\mathrm t\mathrm e\mathrm r}\)
\(\mathrm\Sigma\mathrm m{\mathrm v}_{\mathrm b\mathrm e\mathrm f\mathrm o\mathrm r\mathrm e}=\;\) vector sum of the momenta of all particles before the collision, \(\mathrm\Sigma\mathrm m{\mathrm v}_{\mathrm a\mathrm f\mathrm t\mathrm e\mathrm r}=\) vector sum of the momenta of all particles after the collision
For elastic collisions:
\(\mathrm\Sigma\frac12\mathrm m\mathrm v_{\mathrm b\mathrm e\mathrm f\mathrm o\mathrm r\mathrm e}^2=\;\mathrm\Sigma\frac12\mathrm m\mathrm v_{\mathrm a\mathrm f\mathrm t\mathrm e\mathrm r}^2\)
\(\mathrm\Sigma\frac12\mathrm m\mathrm v_{\mathrm b\mathrm e\mathrm f\mathrm o\mathrm r\mathrm e}^2=\) sum of the kinetic energies before the collision, \(\mathrm\Sigma\frac12\mathrm m\mathrm v_{\mathrm a\mathrm f\mathrm t\mathrm e\mathrm r}^2=\) sum of the kinetic energies after the collision