Speed

Speed: Definition and Mathematical Representation

Introduction

Speed is a fundamental concept in kinematics that refers to how fast an object is moving, regardless of its direction. Unlike velocity, speed is a scalar quantity, meaning it has magnitude but no direction.

Speed helps us understand how quickly an object covers distance over time.

Definition

The instantaneous speed is the magnitude of the velocity vector:

$\text{Speed}=|\overrightarrow{v}|$

For average speed over a finite time interval:

$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$

SI Unit

The SI unit of speed is:

$\mathrm{m}/\mathrm{s}\text{(meters per second)}$

Other commonly used units include:

• Kilometers per hour (km/h)
• Miles per hour (mph)
• Centimeters per second (cm/s)

Speed vs. Velocity

• Speed is a scalar (only magnitude).
• Velocity is a vector (magnitude + direction).

Example: If an object moves in a circle and returns to its starting point, the average velocity is zero, but the average speed is not.

Constant and Variable Speed

• Uniform (Constant) Speed: The object covers equal distances in equal intervals of time.
• Non-uniform Speed: The object covers unequal distances in equal time intervals.

Graphical Interpretation

• The slope of a distance-time graph gives speed.
• The area under a speed-time graph gives distance.

Related Formulas

• When speed is constant:

$s=vt$

Where:

• $s$ is the distance,
• $v$ is the speed,
• $t$ is the time.

• For variable motion, instantaneous speed can be obtained by:

$\text{Speed}=\underset{\mathrm{\Delta }t\to 0}{\lim }\frac{\mathrm{\Delta }s}{\mathrm{\Delta }t}$

Applications

• Road traffic and transportation
• Sports performance (running, cycling, swimming)
• Robotics and automation
• Astronomy (orbital speeds)

See Also

• Velocity
• Acceleration
• Distance
• Displacement
• Kinematics