Final answer:
The device that shows the different driving gears and the selected one in a vehicle is the gear indicator. An odometer measures the total distance traveled, and a speedometer measures instantaneous speed, not velocity. Average speed is calculated by total distance divided by time, while average velocity also considers direction.
Step-by-step explanation:
Gear Indicator and Vehicle Measurements
The device in a vehicle that shows the different driving gears and the one being used is known as the gear indicator. It is distinct from other instruments such as the speedometer, tachometer, and odometer that measure different aspects of the vehicle's operation. A car's odometer measures the total distance traveled by the vehicle, whereas the speedometer measures the vehicle's instantaneous speed, not its velocity. The speedometer does not account for direction, making it a measure of speed only.
When you divide the total distance traveled as determined by the odometer by the trip's time duration, you are calculating the average speed. This is different from the magnitude of the average velocity, which would also consider the displacement or straight-line distance from the starting point to the endpoint. These two quantities, average speed and the magnitude of average velocity, are the same if the trip starts and ends at the same point without changing direction.
Instantaneous velocity and instantaneous speed are closely related; however, velocity also includes direction, making it a vector quantity. The speedometer provides a reading of instantaneous speed at a given moment, while the concept of instantaneous velocity would similarly apply to a single point in time but with directional information included.