Speed and Velocity

Velocity and speed are measures of the change of position of an object over time: 

v = Δx / Δt 

For example, if a car travels 75 meters in three seconds, it has a speed of 25 m/s. 

However, unlike speed, velocities have both a magnitude and a direction. Take the following statement as an example: 

“A car is travelling north at 25 m/s” 

In this statement, 25 m/s is the speed at which the car is travelling, but 25 m/s north is the velocity at which the car is travelling. Quantities that have both magnitudes and directions, like velocity, are called vector quantities. Quantities that only have magnitudes, like speed, are called scalar quantities. Velocities, accelerations, positions, and forces are all vector quantities, with both magnitude and direction. Speed and mass both only have magnitudes, and therefore are scalar properties. When reading equations written on computers, vector quantities are written in bold, while scalar quantities are written in italics. For example, the equation form of Newton’s Second Law is written as:  

F = m a 

… where force and acceleration are vector quantities, and mass is a scalar quantity.  

There is, basically, no such thing as negative mass or negative speed – but there are such thing as negative velocities. Changing the velocity from positive to negative does not change the magnitude of the velocity, but it does change the original direction into the opposite direction! This has an interesting mathematical consequence; consider the following statement:  

A car travels north at 25 m/s for an hour, and then turns around and travels south at 25 m/s for an hour.  

The average speed of the car is 25 m/s, but the average velocity of the car is actually zero! The average velocity of any object is given by:  

v_avg = (x_final – x_initial) / Δt 

And since the car in our example will arrive back where it started after two hours of driving, the average velocity will be zero!