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
  • direction of motion changes
• Average acceleration…
  • is measured over a non-zero time interval
  • is represented by the symbol a_ave or a (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
  • is represented by the symbol a (boldface)
• The various forms of acceleration are defined by the following equations…

  average acceleration		a =  ∆v ∆t
  instantaneous acceleration		a =  lim ∆t→0 ∆v  =  dv  =  d2s ∆t dt dt2

• The SI unit of acceleration is the meter per second squared [m/s²]
• The standard acceleration due to gravity…
  • is a natural unit of acceleration
  • is represented by the symbol g (roman)
  • is equal to 9.806 65 m/s² by definition
  • is often rounded to 9.8 m/s² or even 10 m/s² for convenience
  • is sometimes called the unit of "g force" even though it is a unit of acceleration