Speed and 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
- is represented by the symbol vave or v (vee bar)
- Instantaneous speed…
- is the limit of average speed as the time interval approaches zero
- is the first derivative of distance with respect to time
- 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
- is represented by the symbol vave or v (vee bar)
- Instantaneous velocity…
- is the limit of average velocity as the time interval approaches zero
- is the first derivative of displacement with respect to time
- is represented by the symbol v (boldface)
- The various forms of speed and velocity are defined using the following equations…
average
speedv = ∆s ∆t instantaneous
speedv = lim ∆t→0 ∆s = ds ∆t dt average
velocityv = ∆s ∆t instantaneous
velocityv = lim ∆t→0 ∆s = ds ∆t 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.
∆t → 0 ⇒ v → |v| - The instantaneous speed of an object is the magnitude of its instantaneous velocity.
v = |v|
- Velocity is speed with a direction.
- An object's average speed approaches the magnitude of its average velocity as the time interval approaches zero.
- The SI unit of speed and velocity is the meter per second [m/s].