Speed and Velocity

Describing Motion
Think about a typical school day. In order to attend your classes, visit the school library,
and eat in the cafeteria, you need to change your position. Recall that motion is the
process of changing position. How can you describe how your position changes? There
are different ways to describe an object’s motion. 

Distance and Displacement
Imagine walking from your classroom to the school library. You walk for 10 m, and then
you turn and walk another 20 m. Your motion can be described by the distance you
traveled. Distance is the entire length of an object’s path. The distance you traveled
from the classroom to the school library was 30 m.

Another way to describe how your position changed is by indicating how far you went
from your original position, which is known as displacement. Displacement is the
difference between the initial, or starting, position and the final position. Displacement is
calculated by subtracting the final position of an object from its initial position. For
example, if you walk along a meterstick from 20 cm to 100 cm, your displacement would
be 80 cm.

An object's distance and displacement are not always equal. If an object moves in a
linear, or straight, path in one direction, distance and displacement are equal. For
example, when you walk from 0 cm to 80 cm, your displacement and distance are the
same. However, if you turn around and walk back, your distance traveled will be 160 cm,
and your displacement will be 0 cm.

Displacement and Distance
Two people run 2.0 m in opposite directions from the same spot. Their distance is the
same, but not their displacements. Why? Displacement is a vector. A vector is a quantity
that has both magnitude and direction. A vector's direction can be described in words,
such as “to the right” or “northwest.” 

Arrows are used to represent vectors. The length of the arrow represents the magnitude
of the quantity. The larger the quantity, the longer the arrow. The direction of the quantity
is indicated by the way the arrow points.

Velocity
Another way to describe an object’s motion is to indicate how fast its position changes.
Because position changes can be described in two ways, there are also two ways to
describe how fast an object’s position changes.

Speed and Velocity
When describing an object’s motion, it is common to describe its speed. Speed is a
‘measure of the distance an object travels in a given amount of time. If an object travels
10 m for 5 s, its speed is 2 m/s. This speed, however, does not completely describe the
motion of the object. Was the object moving to the right or to the left? Velocity is the
speed and the direction of a moving object. Because speed and velocity are similar, let's
explore their differences.

Velocity Vectors

The main difference between speed and velocity is that velocity includes the direction of

the object. This makes velocity a vector quantity. Just like displacement, the velocity of

an object is represented using an arrow. The longer the arrow, the faster the object is

moving. The direction of the velocity arrow indicates its direction of motion 

Average Velocity
Similar to speed, the average velocity of an object can be calculated. Average speed is
calculated by dividing total distance by the total time it took to travel that distance.
Average velocity is calculated by dividing the total displacement by the total time it took
to travel that displacement.

Calculating Average Velocity
You can calculate average velocity using the following equation.