Which of the following best describes the difference between average speed and instantaneous speed?

• A. Instantaneous speed is calculated as $\frac{\mathrm{total distance}}{\mathrm{total time}}$, while average speed is the speed at a specific instant.
• B. Average speed and instantaneous speed are always equal for any type of motion.
• C. Average speed is calculated over a time interval as $\frac{\mathrm{total distance}}{\mathrm{total time}}$, while instantaneous speed is the speed at a specific moment in time.
• D. Average speed is always greater than instantaneous speed for any motion.

Answer: (C)

Verified step by step guidance

1. Understand that average speed is defined as the total distance traveled divided by the total time taken. Mathematically, it is expressed as \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\).
2. Recognize that instantaneous speed refers to the speed of an object at a specific moment in time, which can vary throughout the motion.
3. Note that average speed gives an overall measure of how fast an object is moving over a time interval, while instantaneous speed can change from one instant to another during that interval.
4. Realize that instantaneous speed can be found by taking the limit of the average speed as the time interval approaches zero, often using calculus (derivative of position with respect to time).
5. Conclude that the key difference is: average speed is calculated over a finite time interval using total distance and total time, whereas instantaneous speed is the speed at a precise instant.