Describing Motion Around Us

Motion is the change in an object's position over time. This cheat sheet covers linear motion, displacement, speed, velocity, acceleration, and graphical representations of motion.

Core Principles

Position is described by distance and direction relative to a reference point.
Motion occurs when an object's position changes with time.
Displacement is the net change in position, while distance is the total path length.
Average speed is total distance divided by time; average velocity is displacement divided by time.
Acceleration is the rate of change of velocity.
Position-time and velocity-time graphs visually represent motion and its characteristics.

Formulas

$v_{avg} = \frac{\text{total distance travelled}}{\text{time interval}}$
$v_{avg} = \frac{\text{change in position}}{\text{time interval}} = \frac{s}{t}$
$a_{avg} = \frac{\text{change in velocity}}{\text{time interval}} = \frac{v-u}{t}$
$v = u + at$
$s = ut + \frac{1}{2}at^2$
$v^2 = u^2 + 2as$
$v_{avg} = \frac{2\pi R}{T}$