:PROPERTIES: :ID: 80ae7654-34d0-449e-a305-2e5b7512410e :mtime: 20231007011821 :ctime: 20231007011528 :END: #+title: Kinematics #+filetags: :public:project: * Definition Kinematics is the mathematics of describing the motion of physical objects using Newtonian mechanics. * Common Notations in kinematics Here is some common notation used in kinematics: $\vec{r}(t)$ is a position [[id:5864974d-0edf-4757-9b1f-31b159c9aa7a][vector]] of our object $P$, parametrized by some time $t$. The velocity of $P$ is $\vec{u}(t) = \lim_{\delta t \to 0} \frac{\vec{r}(t+\delta t) - \vec{r}(t)}{\delta t} = \frac{d\vec{r}}{dt}$. $\vec{u}$ is also a [[id:5864974d-0edf-4757-9b1f-31b159c9aa7a][vector]], and has units of distance/time The acceleration of $P$ is $\vec{a}(t) = \frac{d\vec{u}}{dt} = \frac{d^{2}\vec{r}}{dt^2} * Common Misconceptions $\vec{u}$ and $\vec{a}$ are not necessarily parallel.