Question

A boy moves on a rectangular track ABCD of length 4m and breadth 3m. He completes 5 and half rounds of the track. Calculate the distance and the displacement.

Answer 1

Solution :

⏭ Given:

✏ A body moves on a rectangular track ABCD of length 4m and breadth 3m.

⏭ To Find:

✏ Distance travelled and displacement after five and half rounds of the track.

⏭ Concept:

✏ Distance is defined as total length of path which is covered by moving body whereas displacement is defined as the shortest distance between initial and final position of journey.

⏭ Calculation:

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• Distance travelled

$\dashrightarrow \sf \: \red{total \: length \: of \: path = 2(l + b)} \\ \\ \dashrightarrow \sf \: distance = 5.5 \times 2(l + b) \\ \\ \dashrightarrow \sf \: distance = 5.5 \times 2(4 + 3) \\ \\ \dashrightarrow \sf \: distance = 5.5 \times 2(7) \\ \\ \dashrightarrow \sf \: distance = 5.5 \times 14 \\ \\ \dashrightarrow \: \boxed{ \tt{ \purple{distance = 77 \: m}}}$

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• Displacement

$\rightarrowtail \sf \: \green{displacement(AC) = \sqrt{ {(AB)}^{2} + {(BC)}^{2} }} \\ \\ \rightarrowtail \sf \: displacement = \sqrt{ {4}^{2} + {3}^{2} } \\ \\ \rightarrowtail \sf \: displacement = \sqrt{16 + 9} \\ \\ \rightarrowtail \sf \: displacement = \sqrt{25} \\ \\ \rightarrowtail \: \boxed{ \tt{ \orange{displacement = 5 \: m}}}$

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⏭ Additional Information:

• Distance is scalar quantity.
• Displacement is vector quantity.
• Vector quantity has both magnitude as well as direction.

Answer 2

A boy moves on a rectangular track ABCD of length 4m and breadth 3m. He completes 5 and half rounds of the track. Calculate the distance and the displacement.

Distance = 77m

Displacement = 5cm