Speed is the total distance covered per unit time — a scalar quantity (no direction). Velocity is the displacement per unit time — a vector quantity (has both magnitude and direction). A body moving in a curved path may have constant speed but changing velocity.
Speed = distance/time (scalar); Velocity = displacement/time (vector).
Speed is always ≥ 0; velocity can be negative.
Speed = |velocity| only for straight-line one-directional motion.
A body in circular motion can have constant speed but changing velocity.
SI unit of both speed and velocity is m/s.
Average speed ≥ |average velocity| for any motion.
Property | Speed | Velocity Definition | Distance covered per unit time | Displacement per unit time Type | Scalar | Vector Formula | Speed = Distance / Time | Velocity = Displacement / Time Direction | No direction | Has direction Value | Always positive (or zero) | Can be positive, negative, or zero SI unit | m/s | m/s Symbol | v or s | v (with arrow) or bold v Can it be zero? | Yes (when at rest) | Yes (when at rest or displacement = 0)
Formulas: Average speed = Total distance / Total time Average velocity = Total displacement / Total time
Example 1: A car completes a circular track of circumference 400 m in 20 s. • Speed = 400/20 = 20 m/s • Displacement = 0 (returns to start) • Velocity = 0/20 = 0 m/s → Speed = 20 m/s, Velocity = 0 m/s
Example 2: A person walks 30 m east then 30 m west in 60 s. • Distance = 60 m; Speed = 60/60 = 1 m/s • Displacement = 0 m; Velocity = 0 m/s
Example 3: A car travels 60 km north in 1 hour. • Speed = 60 km/h • Velocity = 60 km/h north → Both are equal in magnitude when motion is in a straight line.
Key insight: • Speed ≥ |Velocity| always • Speed = |Velocity| only for straight-line motion in one direction • Speed can never be negative; velocity can be negative (motion in opposite direction)
Uniform speed: speed remains constant. Uniform velocity: both speed and direction remain constant.
Example: • A car moving in a circle at constant speed → uniform speed but NOT uniform velocity (direction changes continuously). • A car moving in a straight line at constant speed → uniform velocity.
Instantaneous speed vs instantaneous velocity: • Instantaneous speed = magnitude of instantaneous velocity at that instant. • Speedometer reads instantaneous speed.
Relation between average speed and average velocity: Average speed ≥ |Average velocity| Equality holds only when motion is in one direction throughout.
Speed is a scalar quantity equal to distance/time; it has no direction. Velocity is a vector equal to displacement/time; it has direction. Speed is always positive; velocity can be negative.
Yes. A body moving in a circle returns to the start, so displacement = 0, giving zero average velocity. But it covers distance, so speed is non-zero.
Both have SI unit m/s (metres per second).
Instantaneous speed equals the magnitude of instantaneous velocity. But average speed ≥ |average velocity|; they are equal only for straight-line motion in one direction.
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