Speed

 ( Physical Quantities ) 

In mathematical terms, the instantaneous speed $v$ is defined as the magnitude of the instantaneous velocity $\backslash boldsymbol\{v\}$, that is, the derivative of the position $\backslash boldsymbol\{r\}$ with respect to time: $$v\; =\; \backslash left|\backslash boldsymbol\; v\backslash right|\; =\; \backslash left|\backslash dot\; \{\backslash boldsymbol\; r\}\backslash right|\; =\; \backslash left|\backslash frac\{d\backslash boldsymbol\; r\}\{dt\}\backslash right|\backslash ,.$$

If $s$ is the length of the path (also known as the distance) travelled until time $t$, the speed equals the time derivative of $s$: $$v\; =\; \backslash frac\{ds\}\{dt\}.$$

In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to $v\; =\; s/t$. The average speed over a finite time interval is the total distance travelled divided by the time duration.

Average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the entire distance covered divided by the total time of travel), and so average speed is often quite different from a value of instantaneous speed. If the average speed and the time of travel are known, the distance travelled can be calculated by rearranging the definition to $$d\; =\; \backslash boldsymbol\{\backslash bar\{v\}\}t\backslash ,.$$

Using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres.

Expressed in graphical language, the slope of a tangent line at any point of a distance-time graph is the instantaneous speed at this point, while the slope of a chord line of the same graph is the average speed during the time interval covered by the chord. Average speed of an object is Vav = s÷t

The big difference can be discerned when considering movement around a circle. When something moves in a circular path and returns to its starting point, its average velocity is zero, but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by considering only the displacement between the starting and end points, whereas the average speed considers only the total distance travelled.

• metres per second (symbol m s⁻¹ or m/s), the SI derived unit;
• kilometres per hour (symbol km/h);
• miles per hour (symbol mi/h or mph);
• knots ( per hour, symbol kn or kt);
• feet per second (symbol fps or ft/s);
• Mach number (dimensionless), speed divided by the speed of sound;
• in natural units (dimensionless), speed divided by the speed of light in vacuum (symbol c = ).

• Air speed
• List of vehicle speed records
• Typical projectile speeds
• Speedometer
• V speeds

• P.G. Hewitt (2025). 9788131715536, Pearson Education. . ISBN 9788131715536
• Richard Feynman, Robert B. Leighton, Matthew Sands. The Feynman Lectures on Physics, Volume I, Section 8–2. Addison-Wesley, Reading, Massachusetts (1963). .