Velocity & Acceleration

How do you calculate average velocity?

$$\bar{v} = \frac{x_{2} - x_{1}}{t_{2} - t_{1}}=\frac{\Delta \ x}{\Delta \ t}$$ (60.3)

$$v_{o} = \frac{v_{o}+v}{2}$$ (60.4)

Average velocity ($\bar{v}$) is the total displacement over the total time, e.g. the average speed for an entire road trip (Equation 59.3). Equation 59.4 is another approach to calculating average velocity provided that acceleration is held constant ($v_{o}$ is the velocity at the beginning and $v$ is the velocity at the end).

How do you calculate instantaneous velocity?

$${v} = \lim_{\Delta t\to\infty} \frac{\Delta \ x}{\Delta \ t}$$ (60.5)

Instantaneous velocity ($v$) is average velocity over an infinitesimally small time interval, e.g. the actual speed you see on your speedometer when you are on the highway (Note the difference in notation between average velocity ($\bar{v}$) and instantaneous velocity ($v$).).

How is velocity related to acceleration and time (at constant acceleration)?

$$v = v_{o} + at$$ (60.6)

Where $v_{o}$ is the velocity at the beginning and $v$ is the velocity at the end.