1D Motion

Note: The topic is quite abstract, I spent a lot of time to understand it. Representation of a 1D motion, or a motion along a straight line.

Components

1. Displacement: change of position $\Delta x=\text{final}-\text{initial position}$
2. Average velocity: $v_{av}=\frac{\Delta x}{\Delta t}\text{ (m/s)}$
3. Instantaneous velocity: $v={\lim }_{\Delta t\to 0}\left(\frac{\Delta x}{\Delta t}\right)=\frac{dx}{dt}\text{ (m/s)}$
4. Average acceleration: $a_{av}=\frac{\Delta v}{\Delta t}\text{(m/}{s}^2)$
5. Instantaneous acceleration: $a={\lim }_{\Delta t\to 0}\left(\frac{\Delta v}{\Delta t}\right)=\frac{d^{2}x}{d^{2}t}\text{(m/}{s}^2)$

Free fall case

In the special case of free fall, the acceleration is a constant, $a=g\approx 9.8\text{ (m/}{s}^2)$.