Motion in A Plane

Physics Part I

Physics

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On an open ground, a motorist follows a track that turns to his left by an angle of 600Â after every 500 m. Starting from a given turn, specify the displacement of the motoristÂ at the third, sixth and eighth turn. Compare the magnitude of the displacement withÂ the total path length covered by the motorist in each case.

The path followed by the motorist is a regular hexagon with side 500 m, as shown in the given figure.

Let the motorist start from point P.

The motorist takes the third turn at S.

âˆ´ Magnitude of displacement = PS = PV + VS = 500 + 500 = 1000 m

Total path length = PQ + QR + RS = 500 + 500 +500 = 1500 m

The motorist takes the sixth turn at point P, which is the starting point.

âˆ´ Magnitude of displacement = 0

Total path length = PQ + QR + RS + ST + TU + UP

Â Â Â Â Â Â Â Â Â Â Â = 500 + 500 + 500 + 500 + 500 + 500

Â Â Â Â Â Â Â Â Â Â Â = 3000 m

The motorist takes the eight turn at point R.

âˆ´ Magnitude of displacement = PR

Â

Therefore, the magnitude of displacement is 866.03 m at an angle of 30Â° with PR.

This implies AC makes an angle 30Â° with the initial direction.

Total path length = 8 Ã— 500 = 4000 m.Â

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.

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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.Â

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