Speed is the magnitude of velocity. Is average speed the magnitude of average velocity? Explain your answer.
The Correct Answer and Explanation is:
Correct Answer:
No, average speed is not necessarily the magnitude of average velocity.
Explanation:
Speed is defined as the magnitude of instantaneous velocity. In other words, at any specific moment, speed tells you how fast an object is moving without considering direction. Velocity, on the other hand, is a vector quantity that includes both magnitude and direction.
When we talk about average speed, it is calculated as the total distance traveled divided by the total time taken. Distance is a scalar quantity, meaning it only accounts for how much ground an object has covered, regardless of direction.
Average velocity is calculated as the displacement divided by the total time taken. Displacement is a vector quantity that represents the straight-line distance between the starting point and the final position, including direction.
Since average speed depends on the total distance traveled and average velocity depends on displacement, the two can have different values. In particular, if an object moves along a curved path or changes direction during motion, the total distance will be greater than the displacement. As a result, the average speed will be greater than the magnitude of average velocity in such cases.
However, if an object moves in a straight line in a single direction without reversing, the total distance and displacement will be equal. In that special case, the average speed will be equal to the magnitude of the average velocity.
To summarize, average speed is generally greater than or equal to the magnitude of average velocity. They are only equal when the motion occurs along a straight line without any change in direction. Thus, it is incorrect to say that average speed is always the magnitude of average velocity.
