Explain clearly, with examples, the distinction between : (a) mag… - Vidyadip

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 over 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 quality sign true? [For simplicity, consider one-dimensional motion only].

✓

Answer

(a) The magnitude of displacement means the total length of the line i.e. the distance between the initial and final points. Suppose a body travels from A to B on a linear path and comes back to A. In this case distance = AB + BA = 2AB but displacement = zero.

(b) If the time taken for the body to come back to A is t
$\begin{array}{l}\text { mean speed }=\frac{2 AB }{ t } \\ \text { and mean velocity }=\frac{0}{ t }=0\end{array}$
And the magnitude of mean speed is greater than the magnitude of mean velocity.
$\mid$ Mean speed $|>|$ Mean velocity $\mid$
The magnitude of displacement will be maximum when the body moves in a straight line path without changing direction.

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