If a ball rolls at 2 feet per second, it’s average velocity is two feet per second, and its average velocity is 2 feet per second. At any given moment, however, the object is going faster or slower. This can be expressed as a fraction

2 Feet OR 2 feet/1 second

1 Second

It is important to recognize that the numerator and and denominator are units and not numbers.

The average velocity is 4 feet per second after it has traveled two feet.

In the third second, it covers 18 feet with an average velocity of 6 feet per second.

Notice that after 4 seconds, the average speed is 8 feet per second and after 5 seconds the average speed is 10 feet per second. Notice the pattern of the gain of 2 feet per second of velocity every second.

Velocity of an object increases over time just like speed. Since velocity is speed in a certain direction, velocity increases with the object’s speed.

A “Vector Quantity” is a value or quantity of something directed in a given direction. A “Scalar Quantity” is a vector quantity without a given direction. Velocity is a vector quantity. An object with velocity has to have a given direction. Speed is a scalar quantity. Speed can be in any direction turning or rotating speed is “ignorant of direction”. 50 miles per hour is a speed. 50 miles per hour does not indicate any direction or time. 6 feet per second falling downward is a velocity. Speed and Velocity are therefore not the same.

The average speed is also calculated by the distance traveled divided by the time traveled. The average velocity is equal

(Δ x position) / time

or one can also consider velocity as

displacement / time

For example, A car travels from one city to another city 70 miles (112.6 km) due north. The two cities are connected by a winding road 90 miles (144.8 km) long. If the trip takes 2 hours, the car will have an average speed of 45 miles per hour (72.4 km/h) and an average velocity of 35 miles per hour (56.3 km/h) north.

Complete a test to see if you understand:

1. Which object has a greater velocity, a ball rolling down a 3.4 meter hill in six seconds or a fish swimming upstream and covering 5.4 meters in 0.4 minutes?

2. If Seneca decides to walk across town to a store that is .95 kilometers away and she has only 25 minutes to get there, what speed does she need to maintain to arrive on time?

3. If a projectile flies north 387 meters in 5.8 seconds, what is its velocity?

4. Calculate the velocity of a mountain climber if that climber is moving northeast at a pace of 1.6 km in 1.4 hours? Give your answer in the SI unit for velocity.