Acceleration

Summary

• Acceleration is the rate of change of velocity with time.
  • As a vector it must be stated with both magnitude and direction.
• Acceleration occurs anytime an object's…
  • speed increases,
  • speed decreases, or
  • direction of motion changes.
• Average acceleration…
  • is measured over a non-zero time interval and
  • is represented by the symbol a_ave or a̅ (overline)
• Instantaneous acceleration…
  • is the limit of average acceleration as the time interval approaches zero,
  • is the first derivative of velocity with respect to time,
  • is the second derivative of displacement with respect to time, and
  • is represented by the symbol a (boldface)
• The various forms of acceleration are defined by the following equations…

  average acceleration	a̅ =  Δv Δt
  instantaneous acceleration	a =  lim Δv  =  dv  =  d2r Δt→0 Δt dt dt2

• The SI unit of acceleration is the meter per second squared [m/s²]
• The acceleration due to gravity…
  • is a natural unit of acceleration,
  • is represented by the symbol g (roman),
  • is equal to 9.80665 m/s² by definition,
  • is often rounded to 9.8 m/s² for convenience, and
  • is sometimes called the "g force" even though it is not a measure of force.