Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position of the object during its motion, but also how fast it is moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position x_i, we assign a particular time t_i. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity. This vector quantity is simply the total displacement between two points, Δx, divided by the time taken to travel between them, Δt. The average velocity is a vector and can be positive or negative, depending on the initial and final positions. The expression for the average velocity is given by:

Average speed, meanwhile, is the total distance traveled divided by the elapsed time, and is not necessarily the same as the magnitude of the average velocity. For example, if a trip starts and ends at the same location, the total displacement is zero, and therefore the average velocity is zero. The average speed, however, is not zero, because the total distance traveled is greater than zero. If we go on a road trip of 300 km and need to be at our destination at a certain time, then we would be interested in our average speed. A car’s odometer measures the total distance traveled. So the total distance traveled by the car divided by the total time gives the average speed of the car.

For example, the Shanghai Maglev train connects Longyang Road to Pudong International Airport, which is a distance of 30 km. The journey takes 8 minutes on average. What is the Maglev train’s average velocity?

The known quantities are the distance and time. The unknown quantity, the average velocity, is the total distance divided by the time. Thus, the Maglev train’s average velocity is 225 km/hr.

This text is adapted from Openstax, University Physics Volume 1, Section 3.1: Position, Displacement, and Average Velocity.