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A particle moves so that its position v...

A particle moves so that its position vertor is given by `overset rarr(r ) = cos omegat hatx + sin omegat haty`, where `omega` is a constant. Which of the following is true?

A

Vclocity and acceleration both are
perpendicular to `overset rarr r`

B

Velocity and acceleration both
are parallel to `overset rarr r`

C

Velocity is perpendicular to `overset rarr r`
and acceleration is directed towards the origin

D

Velocity is perpendicular to `overset rarr r`
and acceleration is directed away from the origin

Text Solution

Verified by Experts

The correct Answer is:
C
`overset rarr r= cos omega t overset ^x + sin omega t overset ^y`
`overset ^ v=- omega sin omega t overset ^x + omega cos omega t overset^y`
`overset rarr a = -omega^(2) cos omega t overset ^x+omega^(2)(-sin omega t)overset ^y`
`= - omega^(2)overset rarr r`
`overset rarr r. overset rarr v=0` hence `overset rarr r bot overset rarr v`
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