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# Definiciones
La cinemática describe el **movimiento** de un punto, esta posición dependerá de una magnitud.
- **Vector** **posición**, dependerá de un escalar
$$
\huge \vec{r}(t)=x(t)\vec{i}+y(t)\vec{j}+z(t)\vec{k}
$$
- **Vector** **desplazamiento**, dependerá de un vector
$$
\huge \Delta\vec{r}=\Delta x\vec{i} +\Delta y\vec{j}+\Delta z\vec{k}
$$
- **Velocidad** **media**, relación entre un desplazamiento y el incremento de tiempo
$$
\huge \vec{v}_m=\frac{\Delta\vec{r}}{\Delta t}
$$
- **Velocidad instantánea**, variación de posición en un instante de tiempo : Tangente de la trayectoria
$$
\huge \vec{v} = \lim_{\Delta t \to 0} \frac{\Delta \vec{r}}{\Delta t}
= \frac{d\vec{r}}{dt}
= \frac{dx}{dt} \vec{i} + \frac{dy}{dt} \vec{j} + \frac{dz}{dt} \vec{k}
= v_x \vec{i} + v_y \vec{j} + v_z \vec{k}
$$
- **Aceleración** **media**, relación entre la variación de velocidad y el incremento de tiempo
$$
\huge \vec{a}_m = \frac{\Delta \vec{v}}{\Delta t}
$$
>[!NOTE] Nota
>Sabiendo r(t) podemos obtener v(t) y con esta a(t), derivando
>De la misma manera podemos saber de a(t) a v(t) a r(t), integrando
# Aceleración constante
![[../Pasted image 20250909095158.png]]
# Movimiento Circular
- Coordenadas cartesianas (x, y)
- Coordenadas polares (r, ang)
>[!NOTE] Nota
>Relación entre las coordenadas es:
>$x=r\cos(\theta)$
>$y=r\sin(\theta)$
r(t) = R constant
ang(t) variable

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