Motion in a straight line is one dimensional.

Kinematics or the physics of motion has 4 noteworthy parameters: time ($t$), position ($x$), velocity ($v$), and acceleration ($a$). 

Kinematic problems have a start and end of motion.

# Displacement

Displacement is calculated with the formula:
$$\Delta x = \text{x-value of final position} - \text{x-value of initial posiion}$$

# Velocity
Average velocity over a time interval $\Delta t$ is defined to be: **the displacement** (net change in position), **divided by** **the time taken**.

$$ \bar{v} = \dfrac{\text{final position-initial position}}{\text{final time - initial time}} = \dfrac{x_2 - x_1}{t_2 - t_1} = \dfrac{\Delta x}{\Delta t}$$
**Speed (m/s)** is defined to be the total distance traveled divided by the time taken. Speed and velocity are *not the same*. 


$$ v_{\text{instant}} = v = \lim_{\Delta t \to 0}\frac{\Delta x}{\Delta t} = \frac{dx}{dt}$$
- $x(t)$ -> position as a function of time