A particle moves so that its position vector is given by r → = c o s ω t x ^ + s i n ω t y ^ , where ω is a constant. Which of the following is true?

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Aicharya · Accepted Answer

Position vector is, r → = cos ⁡ ω t x ^ + sin ⁡ ω t y ^ Velocity of particle is v → = d r → d t v → = -sinω t × ω x ^ + cosω t × ω y ^ ⇒ v → = ω - sinω t x ^ + cosω t y ^ Acceleration of the particle is a → = d v → d t ⇒ a → = - ω 2 cosω t x ^ + sinω t y ^ ⇒ a → = - ω 2 r → , So direction of r → and a → are opposite. As v → · a → = 0 ⇒ v → ⊥ a → and v → · r → = 0 ⇒ v → ⊥ r → , So, velocity is perpendicular to r → and acceleration is directed towards the origin.

A particle moves so that its position vector is given by r → = c o s ω t x ^ + s i n ω t y ^ , where ω is a…

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