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Question

Position vector of a particle is given by r=acosωt^i+asinωt^j. Which of the following is/are true?

A
velocity vector is parallel to position vector
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B
velocity vector is perpendicular to position vector
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C
acceleration vector is directed towards the origin
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D
acceleration vector is directed away from the origin
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Solution

The correct options are
B velocity vector is perpendicular to position vector
C acceleration vector is directed towards the origin
r=acosωt^i+asinωt^j
velocity=v=drdt=aωsinωt^i+aωcosωt^j
Acceleration=d2rdt2=aω2cosωt^iaω2sinωt^j=ω2r

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