the magnitude of displacement of a particle is a.is equal to the path length of the particle between two points
Answers
If there is a motion of the particle in one dimension i.e. along a straight line, then the magnitude of displacement becomes equal to total path length traversed by the particle in the given time. As, (AB+BC)> AC, so average speed is greater than the magnitude of average velocity.
Explanation:
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.