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Uniform velocity

Velocity is uniform when equal distances along a straight line are traversed in equal intervals of time. In this case

v = s/t

where

  • v is uniform velocity
  • s is the distance traveled (displacement)
  • t is an interval of time

What about the direction?

Because uniform velocity occurs along a straight line, the computations involving uniform velocity, distance, and time may notnecessarily include the direction of that straight line. However, since both displacement and velocityare vector quantities, it is understood that the direction of velocity is the same as the direction of the displacement.

On the other hand, as you will see later, when combining two or more uniform velocities into a single resultant velocity, the directions of thedifferent uniform velocities becomes extremely important.

Speed, distance, and time

Note also that this same equation can be applied to computations involving speed, distance, and time where

  • v represents speed and not velocity
  • s is the distance traveled (not necessarily in a straight line)
  • t is an interval of time

Units of velocity

The units of velocity are units of distance (such as meters) divided by units of time (such as seconds).

Discussion and sample code

A simple exercise on uniform velocity

Let's begin this section with a short exercise involving uniform velocity.

How long does it take an airplane traveling at a uniform velocity of 350 miles per hour to traverse a distance of 700 miles?

Please copy the code shown in Listing 1 into an html file and open the file in your browser.

Listing 1 . A simple exercise on uniform velocity.
<!---------------- File JavaScript01.html ---------------------><html><body><script language="JavaScript1.3">document.write("Start Script" + "<br/>") var velocity = 350;//uniform velocity in miles/hourvar distance = 700;//miles var time = distance/velocity;//miles/(miles/hour) = hoursdocument.write("uniform velocity = " + velocity + " miles/hour<br/>"); document.write("distance = " + distance + " miles<br/>"); document.write("time = " + time + " hours<br/>"); document.write("End Script")</script></body></html>

Screen output

The text shown in Figure 1 should appear in your browser window when you open the html file in your browser.

Figure 1 . Screen output for Listing #1.
Start Script speed = 350 miles/hourdistance = 700 miles time = 2 hoursEnd Script

Analysis of the code

The equation given earlier that shows the relationship among uniform velocity, distance, and time can be manipulated algebraically tofind any one of the three terms when the values of the other two terms are known. The objective in this exercise is to find the time required to traverse a known distance witha known uniform velocity.

Algebraic manipulation of the equation

Multiplying both sides of the equation by t and dividing both sides by v allows us to rewrite the equation as

t = s/ v

where

  • v is uniform velocity
  • s is the distance traveled
  • t is an interval of time

The solution to the problem is...

This version of the equation is used in Listing 1 to solve for the time required to traverse 700 miles at a uniform velocity of 350 miles/hour. Theanswer is 2 hours as shown in Figure 1 .

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Source:  OpenStax, Game 2302 - mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
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