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Distinguishing Average Speed and Average Velocity

In physics, there is a difference between average speed and average velocity. Say, for example, that while you were driving in Ohio on a cross-country trip, you wanted to make a detour to visit your sister in Michigan after you dropped off a hitchhiker in Indiana.

A trip from Ohio to Michigan.
A trip from Ohio to Michigan.

Your travel path may have looked like the straight lines in this figure — first 80 miles to Indiana and then 30 miles to Michigan.

If you drove at an average speed or a uniform speed of 55 miles per hour and you had to cover 80 + 30 = 110 miles, this trip took you 2.0 hours. But if you calculate the magnitude of the average velocity (by taking the distance between the starting point and the ending point, about 85 miles as the crow flies), you get

image1.png

The direction of the average velocity is just the direction between the start and end points. But if you’re interested in your average speed along either of the two legs of the trip, you have to measure the time it takes for a leg and divide the length of that leg by that time to get the average speed.

To calculate the average speed over the whole trip, you look at the whole distance traveled, which is 80 + 30 = 110 miles, not just 85 miles. And 110 miles divided by 2.0 hours is 55 miles per hour; this is your average speed.

As another illustration of the difference between average speed and average velocity, consider the motion of the Earth around the sun. The Earth travels in its nearly circular orbit around the sun at an enormous average speed of something like 18 miles per second! However, if you consider one full revolution of the Earth, the Earth returns to its original position, relative to the sun, after one year. After one year, there’s no displacement relative to the sun, so the Earth’s average velocity over a year is zero, even though its average speed is enormous!

When considering motion, it’s not only speed that counts but also direction. That’s why velocity is important: It lets you record an object’s speed and its direction. Pairing speed with direction enables you to handle cases like cross-country travel, where the direction can change.

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