Velocity

Claimed by Stacey Nduati.

What is velocity?

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).

Example

3 hour, 230-mile trip

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 north	90 mph north	60 mph north

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. It is important to note that as [math]\displaystyle{ {\Delta\mathit{t}} }[/math] gets very small, the average velocity approaches the instantaneous velocity.

Given the example: The average velocity would be (230 miles/3 hours) = 76.67 mph north.

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.

Connectedness

Velocity is a very interesting and important topic. Take into consideration pilots. flying an aircraft Pilots must combat strong winds while they are thousands of feet up in the air. It is not very useful for a pilot to know that the wind is traveling at 80 mph. What direction is it traveling in? The direction of this wind could prove to be useful, or to be a nightmare for the pilot! Pilots must know whether they are flying with the wind, or against the wind.

Also, take into consideration sports. In baseball, when the pitcher throws the ball to the batter, the batter must make a decision as to what he/she wants the ball's velocity to be. The ball can either go fast or slow (magnitude), or left or right (direction), etc. This immediate decision plays a huge role in how each team will increase their score during the game.

See Also

Relative Velocity

Speed and Velocity

Terminal Speed

References

1. Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. Hoboken, NJ: Wiley, 2011. Print.

2. "Velocity." Def. 2. Dictionary.com. N.p., n.d. Web. 29 Nov. 2015.

3. Velocity Expression. Digital image. Physics-Formulas. N.p., n.d. Web. 29 Nov. 2015.

4. Animated Car On Road. Digital image. Clip Art Best. N.p., n.d. Web. 29 Nov. 2015.

External links

The Physics Classroom: Speed and Velocity

HyperPhysics: Average Velocity