## Wednesday, September 1, 2021

### Finding Average Velocity

Physics Index

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 • t

dividing both sides by t yields

∆d/t = vave

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

d = vt
d/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 • t
df - 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.