<p align="right">Last Update: <font color="#4f81bd">July, 25, 2024</font></p> ## BIG IDEAS - Also known as uniform motion. - The speed or direction of the object does not change; that is, the object moves at a constant rate. - The position of the object changes linearly with time. - A constant velocity (including rest) indicates balanced [[Force|forces]]. ### Equation 1 (Velocity-Time) $\textcolor{red}{ v = \text{constant}}$ $x = x_{0} + \textcolor{red}{v}t \tag{1} $ where $x$ is final position, $x_0$ is initial position, $v$ is velocity, and $t$ is the time interval. ### Derivation Equation 1 is an algebraic rearrangement of the definition of velocity. $\textcolor{red}{v} = \frac{\Delta x}{t} \tag{2}$ where $\Delta x$ is $x - x_0$ $\textcolor{red}{v} = \frac{x - x_{0}}{t} \tag{3}$ Multiply both sides by $t$ $\textcolor{red}{v} \cdot t = x - x_{0} \tag{4}$ Add $x_0$ to both sides $\textcolor{red}{v} \cdot t \ + x_{0} = x \tag{5}$ This is the same as $ \boxed{ \ x = x_{0} + \textcolor{red}{v} \ \cdot t \ } \tag{1}$ --- Return [[Home|Home]] | [[Mechanics]] | [[Notes Vault/Physics Notes Vault/Kinematics/Kinematics]] | [[Notes Vault/Physics Notes Vault/Dynamics/Dynamics]] | [[Notes Vault/Physics Notes Vault/Kinematics/1D Motion/Position|Position]] | [[Displacement]] | [[Speed]]