Final answer:
An odometer measures the distance a vehicle has traveled, and dividing this distance by the time of travel gives the average speed. The speedometer indicates a vehicle's instantaneous speed. Average speed is different from average velocity, which includes a directional component.
Step-by-step explanation:
An odometer is a device used for measuring the distance traveled by a vehicle, such as a car. It does this by recording the number of miles or kilometers that the vehicle has driven since it was first used. Therefore, the correct answer to what an odometer shows is B. the number of miles the vehicle has been driven. When you divide the total distance traveled (as determined by the odometer) by the total time of the trip, you are calculating the average speed, not the magnitude of the average velocity. These two quantities, average speed and magnitude of average velocity, are the same when the trip lacks any change in direction, meaning the start and end points are the same, without any returning.
The speedometer of a car, on the other hand, measures the instantaneous speed, which is the speed of the vehicle at a particular moment in time. The difference between speed and velocity is that velocity includes a direction component, whereas speed does not.