A particle moves such that its position vector r→$$t=$$$$cos$$ωt $$i^+$$$$sin$$ωt $$j^$$ where ω is a constant and t is time. Then which of the following statements is true for the velocity ν→t and a→tacceleration of the particle :

Question

A particle moves such that its position vector r→$$t=$$$$cos$$ωt  $$i^+$$$$sin$$ωt  $$j^$$  where  ω is a constant and t is time. Then which of the following statements is true for the velocity ν→t  and a→tacceleration   of the particle :

Infinity Learn · Accepted Answer

r→$$=$$$$cos$$ωti∧$$+$$$$sin$$ωtj∧​⇒v→$$=dr$$→$$dt=$$ω−$$sin$$ωti∧$$+$$$$cos$$ωtj∧​⇒a→$$=dv$$→$$dt=$$ω$$2$$−$$cos$$ωti∧−$$sin$$ωtj∧⇒a→$$=$$−ω$$2cos$$ωti∧$$+$$$$sin$$ωtj∧​⇒a→$$=$$−ω$$2r$$→​∴a→ is anti parallel to r→r→ is radially outward​So, a→ is radially inward​​Also., v→.r→$$=$$ω−$$sin$$ωtcosω$$t+$$$$cos$$ωtsinω$$t=0So$$ v→ ⊥r→

A particle moves such that its position vector $\vec{r} (t) = \cos ω t \hat{i} + \sin ω t \hat{j}$ where $ω$ is a constant and t is time. Then which of the following statements is true for the velocity $\vec{ν} (t)$ and $\vec{a} (t)$ acceleration of the particle :

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A particle moves such that its position vector r→t=cosωt i^+sinωt j^ where ω is a constant and t is time. Then which of the following statements is true for the velocity ν→t and a→tacceleration of the particle :

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A particle moves such that its position vector $\vec{r} (t) = \cos ω t \hat{i} + \sin ω t \hat{j}$ where $ω$ is a constant and t is time. Then which of the following statements is true for the velocity $\vec{ν} (t)$ and $\vec{a} (t)$ acceleration of the particle :