The Physics
Hypertextbook
Opus in profectus

# 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 aave or (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.