---
tags : Mechanics,Kinematics
title : 2020.4.2(5)
---
# Mechanics(5)
## §1.4 Plane polar coordinates, component in two dementional motion
### Velocity , acceleration in 2,3 dementional space
Write a displacement when the object moves the position **r** at time *t* to **r** (*t*+$\Delta$t) at $\Delta$t by bector

$\large r(t+\Delta t) - r(t)$

We can define velocity **v** in 2,3 dementional space by expanding the velocity in one dementional space to bector

$\large v =\displaystyle\lim_{\Delta t\to \ 0} \frac{r(t+\Delta t)-r(t)}{\Delta t}$

Generally, we express this as

$\large v=\frac{dr}{dt}$

Set as $r=xi+yj+zk$ ,
:::info

$\large v= \frac{dx}{dt}i + \frac{dy}{dt}j + \frac{dz}{dt}k$
:::

In the same way, define acceleration **a**,

$\large a=\displaystyle \lim_{\Delta t\to \ 0} \frac{v(t+\Delta t)-v(t)}{\Delta t}$

and

$\large a= \frac{dv}{dt} = \frac{d^2r}{dt^2}$

and

:::info
$\large a=\frac{d^2x}{dt^2}i + \frac{d^2y}{dt^2}j + \frac{d^2z}{dt^2}k$
:::