For example, if you travel distance s in a time t, your speed, v, is
Speed can take many forms, which you find out about in the following sections.
Reading the speedometer: Instantaneous speed
You already have an idea of what speed is; it’s what you measure on your car’s speedometer, right? When you’re tooling along, all you have to do to see your speed is look down at the speedometer. There you have it: 75 miles per hour. Hmm, better slow it down a little — 65 miles per hour now. You’re looking at your speed at this particular moment. In other words, you see your instantaneous speed.
Staying steady: Uniform speed
What if you keep driving 65 miles per hour forever? You achieve uniform speed in physics (also called constant speed). Uniform motion is the simplest speed variation to describe, because it never changes.
Uniform speed may be possible in the western portion of the United States, where the roads stay in straight lines for a long time and you don’t have to change your speed. But uniform speed is also possible when you drive around a circle, too. Imagine driving around a racetrack; your velocity would change (because of the constantly changing direction), but your speed could remain constant as long as you keep your gas pedal pressed down the same amount. We discuss uniform circular motion in Chapter 7, but in this chapter, we stick to motion in straight lines.
Shifting speeds: Nonuniform motion
Nonuniform motion varies over time; it’s the kind of speed you encounter more often in the real world. When you’re driving, for example, you change speed often, and your changes in speed come to life in an equation like this, where vf is your final speed and vi is your initial speed:
The last part of this chapter is all about acceleration, which occurs in nonuniform motion. There, you see how changing speed is related to acceleration — and how you can accelerate even without changing speed!
Busting out the stopwatch: Average speed
Say, for example, that you want to drive from New York City to Los Angeles to visit your uncle’s family, a distance of about 2,781 miles. If the trip takes you 4.000 days, what was your average speed? You divide the total distance by the change in time, so your average speed for the trip would be
This solution divides miles by days, so you come up with 695.3 miles per day. Not exactly a standard unit of measurement — what’s that in miles per hour? To find it, you want to cancel days out of the equation and put in hours (see Chapter 2). Because a day is 24 hours, you can multiply this way (note that days cancels out, leaving miles over hours, or miles per hour):
That’s a better answer.
Contrasting average and instantaneous speed
If you travel 2,781 miles in 4.000 days (a total of 96 hours), you go at an average speed of 28.97 miles per hour. That answer seems pretty slow, because when you’re driving, you’re used to going 65 miles per hour. You’ve calculated an average speed over the whole trip, obtained by dividing the total distance by the total trip time, which includes non-driving time. You may have stopped at a hotel several nights, and while you slept, your instantaneous speed was 0 miles per hour; yet even at that moment, your overall average speed was still 28.97 miles per hour!
Distinguishing average speed and average velocity
There is a difference between average speed and average velocity. Say, for example, that while you were driving in Ohio on your cross-country trip, you wanted to make a detour to visit your
