Assertion: The speedometer of an automobile measures the average speed of the automobile.

Reason: Average velocity is equal to total distance by total time taken.

Explanation:

To understand the assertion and reason given, let's break it down and analyze it step by step:

Measuring Average Speed:
- The speedometer of an automobile is a device used to measure and display the speed at which the automobile is traveling.
- It is typically located on the dashboard of the vehicle and provides a real-time indication of the speed.
- The speedometer measures the instantaneous speed at any given moment, which is the speed of the automobile at that particular instant.

Understanding Average Velocity:
- Velocity is a vector quantity that includes both speed and direction.
- Average velocity is calculated by dividing the total displacement by the total time taken.
- Displacement refers to the change in position of an object, measured in a straight line from the initial position to the final position.
- Total time taken refers to the time elapsed during the entire journey.

Relationship between Speed and Velocity:
- Speed is a scalar quantity that only considers the magnitude of the motion without considering the direction.
- Velocity, on the other hand, is a vector quantity that takes into account both the magnitude and direction of the motion.
- The speedometer of an automobile measures the speed, which is the magnitude of the velocity, but does not provide information about the direction.

Conclusion:
- The speedometer of an automobile measures the speed of the automobile at any given instant, which is a scalar quantity.
- Average velocity, which takes into account both speed and direction, can be calculated by dividing the total displacement by the total time taken.
- Therefore, the assertion that the speedometer measures the average speed of the automobile is incorrect.
- The reason provided, which states that average velocity is equal to total distance by total time taken, is also incorrect as it overlooks the fact that velocity is a vector quantity that includes direction.