**Where are we going with this?**The information on this page relates to the skills needed to investigate and evaluate the graphical and mathematical relationship (using either manual graphing or computers) of one-dimensional kinematic parameters (distance, displacement, speed, velocity, acceleration) with respect to an object's position, direction of motion, and time.

**Finding Average Velocity**

(Average? That sounds easy!)

The average velocity of an object in motion is pretty common sense. It's the average velocity.

*MEASURING*average velocity is kind of… abstract. So, moving on…

**Calculating Average Velocity**

When we calculate average velocity, we have two options.

**Option one relies on knowing how far an object moved (displacement) and how long it took.**

*NOTE: The ideas are the same for calculating average speed, but you will be looking at distance traveled rather than displacement.*

Given displacement

*∆d*, and elapsed time,*t*, average velocity,*vave*, can be found using the relationship∆d = vave • tdividing both sides by t yields∆d/t =vave

Some sources will simplify the way the formula looks as follows:

d = vtd/t = v

Also, some sources will use

*x*for position and*∆x*for displacement.The above, simple equation, can be complicated by adding extra information. You might have to work through the more complete displacement formula:

To add a bit more detail, we can consider a more complex situation. Where

*df*is final distance/displacement from a reference point and where*di*is the initial displacement/distance,*vave*is average velocity and*t*is elapsed time,df = di + vave • tdf - di = vave • t

(df - di ) / t = vave

**The second method of calculating average velocity assumes an object is changing velocity uniformly over some period of time.**In such a case, finding the average velocity relies on knowing the initial velocity, the final velocity and the period of time that the acceleration was uniform.

In such a case,

vave = (vf + vi)/2

where

*vave*is average velocity,*vf*is final velocity, and*vi*is initial velocity.
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