Calculating Average Speed: Formula & Practice Problems

What is Average Speed?

You and your friend decided to take your brand new red sports car out for a spin. Your car is capable of speeds up to 220 mph. You drove 45 miles in 1.25 hours. At the end of your trip, your friend tells you that your average speed during the trip is 36 miles per hour. You were appalled. You asked yourself, ‘How can a sports car have such a pitiful average speed?’ and tried to recall how much you paid for it. What is average speed anyway?

The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance. It’s a scalar quantity which means it is defined only by magnitude. A related concept, average velocity, is a vector quantity. A vector quantity is defined by magnitude and direction. For example, we might say that a car has an average speed of 25 miles per hour. Its average velocity might be 25 miles per hour due east.

Average speed can be viewed as the rate of change in distance with respect to time. A car traveling at an average speed of 25 miles per hour covers an average distance of 25 miles every hour.

Calculating Average Speed

If an object travels with constant speed, then the formula for the speed of the object is given by,

Total distance is the distance traveled by the object at the constant speed. Elapsed time is the time the object took to cover the total distance. In most instances, an object will travel with varying speeds over a certain distance. For example, a car traveling from one city to another will rarely move at a constant speed. It is more likely that the car’s speed will fluctuate during the trip. The car might travel at 65 mph for some time and then slow down to 25 mph. It’s possible that at certain times, the car is even at full stop (such as, at a red light). To calculate the car’s average speed, we don’t really care about the fluctuations in its speed. We only care about the total distance traveled by the car and the elapsed time to cover that distance.

The formula for average speed is

It’s important to note that this formula is identical to that of constant speed. Average speed is measured in units of distance per time. Common units include miles per hour (mph), kilometers per hour (kph), meters per second (m/s), or feet per second (ft/s).

As for your brand-new red sports car, your friend was exactly right in his calculation of the average speed. He used the distance traveled by the car (45 miles) divided by elapsed time (1.25 hours). The construction on the highway and the series of red lights on the local roads really slowed you down. The high elapsed time resulted in a low average speed.

Examples

Let’s look at some other examples of average speed:

1. Suppose a freight train travels a distance of 120 miles in 3 hours. What is the average speed of the train?

Answer:

Its average speed is

2. Suppose a truck travels in segments that are described in the following table:

What is the average speed of the truck?

Answer:

Based on the information given, its average speed over the four segments can be calculated as

3. A car travels 50 mph on a trip from Chicago, IL, to Minneapolis, MN, and 65 mph on the return trip. What is the average speed of the car for the entire round trip?

Answer: