Most vehicles are not direct drive, so let's look at another type of vehicle: a 3 speed bicycle. A bicycle uses a chain drive. It allows you to move the pedals, and the charin transfers the energy from the pedals to the rear wheel.
The chain glides over different sized sprockets, depending on the speed of the rider. Which sprocket combination will make the rider go the fastest, if the pedaling rate, or, "cadence"is the same? (Hint: how many times will the back sprocket - and therefore the back wheel - turn with each rotation of the front sprocket?)
Each rotation of the front sprocket will make the back wheel rotate once in combo 1, twice in combo 2, and four times in combo 3. So, combination 3 will go the fastest . These sprocket combinations can also be called gear ratios, because the new speed is calculated as the ratio of the driven (front) sprocket over the driver (back) sprocket.
So how does this affect the way a cyclist would pedal the bicycle? Well, when she starts out, she starts in first gear (combo 1). As she pedals faster the bike starts going faster. After a while, her legs are moving very fast, so she switches to second gear (combo 2). Now her legs only go half as fast as before, but the bike is still going fast. She can increase her cadence again and make the bike go even faster. Once her cadence is very high again, she can shift up to third gear (combo 3).
If she was going 5 miles per hour in first gear, how fast is she going in third gear with the same pedaling rate?
Well, the jump from first to second gear doubles the speed, and the step from second to third gear doubles it again.So, she is going four times as fast as in first gear. She is now going 20 miles per hour, but her legs are going the same rate as at the very beginning!
The term "3-speed" bike is not entirely correct because a cyclist can go more than just three different speeds. As we saw in the previous example, our cyclist was able to continuously speed up from 5 mph to 20 mph. But the name comes from the fact that given one cadence, the three gear ratios will give you three different speeds. Of courses your legs can pedal at many different rates but, "3-speed" bike sounds better than "3-gear-ratio" bike.
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