explain with example the distinction between the average velocity over an interval of time and average speed over a same period show that the average speed is eighter greater than or equal to average velocity. when is the equality sign true?
Answers
Answer:
Explanation:
(a) The magnitude of displacement over an interval of time is the shortest distance (which is a straight line) between the initial and final positions of the particle.
The total path length of a particle is the actual path length covered by the particle in a given interval of time.
For example, suppose a particle moves from point A to point B and then, comes back to a point, C taking a total time (t), as shown below. Then, the magnitude of displacement of the particle = AC.
Whereas, total path length = AB+BC.
It is also important to note that the magnitude of displacement can never be greater than the total path length. However, in some cases, both quantities are equal to each other.
(b) Magnitude of average velocity = Magnitude of displacement / Time interval
For the given particle,
Average velocity = AC/t
Average speed = Total path length / Time interval
= (AB+BC)/t
Since, (AB+BC)>AC, average speed is greater than the magnitude of average velocity. The two quantities will be equal if the particle continues to move along a straight line.