Question

Explain clearly with examples, the distinction between:
a. Magnitude of displacement (sometimes called distance) over an interval of time and the total length of path covered by a particle over the same interval.
b. Magnitude of average velocity over an interval of time and the average speed of the same interval.
Average speed of a particle over an interval of time is defined as the total path length divided by the time interval. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity consider one dimensional motion only].

Answer 1

Hii dear,

Suppose a particle moves from point A to point C and then, comes back to a point B, taking a total time t, as shown in figure.

## (a)
# The magnitude of displacement-
It is the shortest distance between the initial and final positions of the particle.
For given particle,
Magnitude of displacement of the particle s = AB.

# The total path length of a particle-
It is the actual path length covered by the particle in a given interval of time.
For given particle,
Total path length l = AC+CB

Here, l > s
Hence, we can say that total path length is always greater than or equal to magnitude of displacement.

## (b)
# Magnitude of average velocity-
For the given particle,
Average velocity = Magnitude of displacement / Time interval
= AB/t

# Average speed-
For the given particle,
Average speed = Total path length / Time interval
= (AC+CB) / t

As, l > s
Hence, we can say that average speed is always greater than or equal to magnitude of velocity.

Hope that helps you.

Answer 2

Suppose a particle moves from point A to point C and then, comes back to a point B, taking a total time t

(a)The magnitude of displacement-

It is the shortest distance between the initial and final positions of the particle.

For given particle,

Magnitude of displacement of the particle s = AB.

The total path length of a particle-

It is the actual path length covered by the particle in a given interval of time.

For given particle,

Total path length l = AC+CB

Here, l > s

Hence, we can say that total path length is always greater than or equal to magnitude of displacement.

(b) Magnitude of average velocity-

For the given particle,

Average velocity = Magnitude of displacement / Time interval

= AB/t

Average speed-

For the given particle,

Average speed = Total path length / Time interval

= (AC+CB) / t

As, l > s

Hence, we can say that average speed is always greater than or equal to magnitude of velocity.