A particle moves so that its position vector is given by $\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y},$ where $ω$ is a constant.
Which of the following is true?

Question

A particle moves so that its position vector is given by r→$$=$$$$cos$$ωt $$x^+$$$$sin$$ωt $$y^$$, where ω is a constant.Which of the following is true?

Infinity Learn · Accepted Answer

Given, r→$$=$$$$cos$$ωt $$x^+$$$$sin$$ωt $$y^$$∴v→$$=dr$$→$$dt=-$$ω$$sin$$ωt $$x^+$$ω$$cos$$ωt $$y^a$$→$$=dv$$→$$dt=-$$ω$$2cos$$ωt $$x^-$$ω$$2sin$$ωt $$y^=-$$ω$$2r$$→ Since position vector (r$$→$$) is directed away from the origin, so,  acceleration $$-$$ω$$2r$$→ is directed towards the origin. also,⇒r→⊥v→r→·v→$$=($$$$cos$$ω$$tx^+$$$$sin$$ω$$ty^)$$·$$(-$$ω$$sin$$ω$$tx^+$$ω$$cos$$ω$$ty^)=-$$ω$$sin$$ωtcosω$$t+$$ω$$sin$$ωtcosω$$t=0$$

A particle moves so that its position vector is given by $\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y},$ where $ω$ is a constant.
Which of the following is true?

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A particle moves so that its position vector is given by r→=cosωt x^+sinωt y^, where ω is a constant.Which of the following is true?

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A particle moves so that its position vector is given by $\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y},$ where $ω$ is a constant.
Which of the following is true?