### Theory:

The shortest distance from the initial to the final position of an object is called displacement. The SI unit of displacement is metre (\(m\)).

*Positions of an object on a straight line path*

For the object to move from \(O\) to \(A\),

Distance covered \(=\) \(60\ km\)

Magnitude of displacement \(=\) \(60\ km\)

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Distance covered in its motion from \(O\) to \(A\) and back to \(B\) \(=\) \(60\ km\) \(+\) \(25\ km\) \(=\) \(85\ km\)

Magnitude of displacement \(=\) \(35\ km\)

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Thus, the magnitude of displacement \(35\ km\) is not equal to the path length \(85\ km\). Hence, the magnitude of the displacement for motion may be zero, whereas the corresponding distance covered during the motion is not zero.

When the object travels back to \(O\), the final position coincides with the initial position and makes the displacement equal to zero.

Distance covered in this journey \(=\) \(OA\) \(+\) \(AO\) \(=\) \(60\ km\) \(+\) \(60\ km\) \(=\) \(120\ km\)

Distance and displacement are the two physical quantities that

**describe the motion**of an object. This also helps to locate its final position with reference to its initial position at a given time.Important!

Distance is a scalar quantity whereas; displacement is a vector quantity.

**Illustration:**

Imagine Anne and Christy going to school from home together. One day Christy decided to reach school after attending her tuition. The path they travelled is given in the figure.

*Route map*

From the above details, can you tell which one took the longer path to reach the school?

Clearly, the path Christy travelled is quite longer than Anne travelled. Therefore, Anne reached the school faster than Christy because Anne travelled in the shortest path.

Important!

The shortest path is the quickest way to travel from one place to another place. Mostly the shortest paths are like a straight-line paths.

In this case, the total distance travelled by Anne from home to school is \(20\ km\), and the total distance travelled by Christy is \(25\ km\). Anne travelled \(20\ km\), which is the shortest distance from home to school.

Though Christy took the longest distance to reach school, she can reach school quicker than Anne, if she travels faster than her.