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

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.

For example: A car takes 3 hours to make a 230-mile trip from Point A to Point B. For the first hour, the car travels at 80 mph east. For the second hour, the car travels at 90 mph north. For the third and final hour, the car travels at 60 mph north. 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.

Looking at the previous 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.

Continuing with the previous 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.

External links

The Physics Classroom: Speed and Velocity

HyperPhysics: Average Velocity