The Physics
Hypertextbook
Opus in profectus

# Speed & Velocity

## Summary

• Speed is the rate of change of distance with time.
• As a scalar it has magnitude only.
• Average speed
• is measured over a non-zero time interval and
• is represented by the symbol vave or (overline)
• Instantaneous speed
• is the limit of average speed as the time interval approaches zero,
• is the first derivative of distance with respect to time, and
• is represented by the symbol v (italic)
• Velocity is the rate of change of displacement with time.
• As a vector it must be stated with both magnitude and direction.
• Average velocity
• is measured over a non-zero time interval and
• is represented by the symbol vave or (overline)
• Instantaneous velocity
• is the limit of average velocity as the time interval approaches zero,
• is the first derivative of displacement with respect to time, and
• is represented by the symbol v (boldface)
• The various forms of speed and velocity are defined by the following equations…
average
speed
 v̅ = Δs Δt

instantaneous
speed
 v = lim Δs = ds Δt → 0 Δt dt

average
velocity
 v̅ = Δr Δt

instantaneous
velocity
 v = lim Δr = dr Δt → 0 Δt dt
• The relation of speed to velocity
• An object's average speed approaches the magnitude of its average velocity as the time interval approaches zero.  Δt → 0 ⇒ v̅ → |v̅|
• The instantaneous speed of an object is the magnitude of its instantaneous velocity.

v = |v|

• The SI unit of speed and velocity is the meter per second [m/s].