Velocity
Claimed by Stacey Nduati.
Velocity is the time rate of change of position of a body in a specified direction. It is a vector quantity that consists of a magnitude and direction. Speed is also the change of position of a body; however, it does not take the object's direction into consideration.
Equation
Average velocity can be calculated using the following equation:
- [math]\displaystyle{ \boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{r}}{\Delta\mathit{t}} }[/math] ,
where [math]\displaystyle{ {\Delta\boldsymbol{r}} }[/math] is the change of position of the object and [math]\displaystyle{ {\Delta\mathit{t}} }[/math] is the change of time.
The SI units for velocity are meters per second (m/s).
Examples
A car takes 3 hours to make a 230-mile trip from Point A to Point B.
| Hour 1 | Hour 2 | Hour 3 | |
|---|---|---|---|
| Velocity | 80 mph | 90 mph | 60 mph |
There are two kinds of velocity in which one must consider: instantaneous velocity and average velocity.
Instantaneous Velocity
Instantaneous velocity is the speed and direction of an object at a particular instant.
Given the example: Each hour has a different instantaneous velocity.
Average Velocity
Average velocity is the net displacement of an object, divided by the total travel time. It is the average of all instantaneous velocities.
Given the example: The average velocity would be (230 miles/3 hours) = 76.67 mph.
Acceleration
Acceleration is the time rate of change of velocity, with the following equation:
- [math]\displaystyle{ \boldsymbol{a} = \frac{\Delta\boldsymbol{v}}{\Delta\mathit{t}} }[/math] ,
where [math]\displaystyle{ {\Delta\boldsymbol{v}} }[/math] is the change of velocity of the object and [math]\displaystyle{ {\Delta\mathit{t}} }[/math] is the change of time.
The SI units for acceleration are meters per second per second (m/s/s). It is also a vector quantity.
Given the example: The acceleration from the 1st hour to the 2nd hour is 10 mph. This indicates a positive acceleration. The acceleration from the 2nd hour to the 3rd hour is -30 mph. This indicates a negative acceleration.
References
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.
"Velocity." Def. 2. Dictionary.com. N.p., n.d. Web. 29 Nov. 2015.