# Velocity

By Eugene Toth
What is Velocity?  Many think velocity is just a scientific name for speed.  They are partially right. Scientist define velocity as distance covered in unit time as in feet per second or miles per hour.

The curve of Force and Velocity. As the force exerted on an object is decreased, the velocity of the object is decreased.

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.