Final answer:
The odometer is the gauge that measures the total distance traveled by a vehicle. In contrast, the speedometer measures the vehicle's instantaneous speed. Other gauges like the fuel gauge work based on the voltage output from sender units.
Step-by-step explanation:
The gauge that tells you how far you've driven is the odometer. An odometer measures the total distance traveled by a vehicle, not its displacement. Displacement refers to the change in position from a starting point, whereas distance measures the total path length taken, regardless of the starting point. In contrast, a car's speedometer measures its instantaneous speed, not velocity. Speed is the rate of movement, while velocity is speed with a direction. The speedometer displays how fast the car is moving at a specific moment without regard to direction.
Regarding other instruments in a car, the fuel gauge indicates the level of gasoline in the tank, and in some cars, like the 1996 Volkswagen referenced, the fuel gauge operates as a voltmeter that measures the voltage output of 'sender' units. These are assumed to be proportional to the amount of gasoline in the tank. Temperature gauges work similarly, providing an indication of the engine's temperature based again on voltage output.
It is worth noting that dividing the odometer reading (total distance) by the time taken for a trip gives you the average speed. Average velocity could only be the same as average speed if the trip starts and ends in the same location, making the displacement zero.