Video 1: Motion

Definitions

Kinematics: The study of describing motion.

Dynamics: The study of the causes of motion.

Terms to describe Linear Motion

Distance ( $d$ )

Position ( $x$ )

Displacement ( $\Delta x$ )

Average Speed ( $S_{avg}$ )

Average Velocity ( $V_{avg}$ )

Instantaneous Speed

Instantaneous Velocity

Average Acceleration

Instantaneous Acceleration

Basic Formulas

S_{avg} = \frac{distance}{time}

\vec V_{avg} = \frac{\Delta x}{\Delta t}

Instantaneous speed is a very, very small distance divided by a very very small time.

V = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}

In other words, velocity is the derivative of position (x) with respect to time (t).

\vec a_{avg} = \frac{\Delta V}{\Delta t}

\vec a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{dv}{dt}

In other words, acceleration is the derivative of velocity ( $\vec v$ ) with respect to time (t).