Speed
Speed is how fast an object moves, calculated as distance divided by time (v = d/t) and measured in meters per second.
Formula
v = \frac{d}{t}
Definition
Speed tells you how fast something is going: the distance traveled divided by the time it took, $v = d/t$. It is a scalar quantity with SI units of meters per second (m/s). Average speed uses total distance and total time, while instantaneous speed is the speed at one moment, like a speedometer reading. Formally, speed is the magnitude of the velocity vector, $v = |\vec{v}|$, so it is always non-negative, and instantaneous speed is $ds/dt$, the time derivative of arc length. Average speed over a trip can differ from the magnitude of average velocity whenever the path is not a straight line.
Example
A dog that runs $20\ \text{m}$ in $4\ \text{s}$ has a speed of $20 \div 4 = 5$ meters per second. A cyclist who rides $1{,}800\ \text{m}$ in $300\ \text{s}$ averages $1800 \div 300 = 6\ \text{m/s}$; multiplying by $3.6$ converts that to $6 \times 3.6 = 21.6\ \text{km/h}$. Averages can be less obvious than they look: a car that drives $60\ \text{km}$ at $30\ \text{km/h}$ (taking $2\ \text{h}$) and then $60\ \text{km}$ at $60\ \text{km/h}$ (taking $1\ \text{h}$) has an average speed of $120 \div 3 = 40\ \text{km/h}$, not $45$, because the slower leg takes more time.
Key Insight
Speed does not care about direction; a car going $30\ \text{mph}$ north and a car going $30\ \text{mph}$ south have the same speed. On a distance-versus-time graph, speed is the slope, so a steeper line means a faster object and a flat line means the object is stopped. Speed also has an outsized effect on energy. Kinetic energy depends on speed squared, so doubling speed quadruples the energy a car must shed to stop, and braking distance grows with the square of speed for exactly this reason.