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 v_ave or v (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 v_ave or v (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 …

  v =  Δs Δt		average speed		v =  lim Δs  =  ds Δt → 0 Δt dt		instantaneous speed
  v =  Δr Δt		average velocity		v =  lim Δr  =  dr Δt → 0 Δt dt		instantaneous velocity

• 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	⇒	v → |v|

  • 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].