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Explain Clearly, with Examples, the Distinction Between 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 - Physics

Explain clearly, with examples, the distinction between 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.

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Solution 1

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.

Solution 2

Suppose a particle goes from point A to B along a straight path and returns to A along the same path. The magnitude of the displacement of the particle is zero, because the particle has returned to its initial position. The total length of path covered by the particle is AB + BA = AB + AB = 2 AB. Thus, the second quantity is greater than the first,

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NCERT Class 11 Physics Textbook
Chapter 3 Motion in a Straight Line
Q 13.1 | Page 57
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