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

Question

A particle moves such that its position vector

r \to (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

v \to (t)

and acceleration

a \to (t)

of the particle:

Accepted Answer

Correct answer: A. (a) r = cos ⁡ ωt i+ sin ⁡ ωt j v = dr dt= (- sin ⁡ ωt i+ cos ⁡ ωt j ) ato =(dvto )/(dt)=-omega 2(cos⁡omega ti+sin⁡ωtj) a =- ^2r ∴a is antiparallel to r v r = (- sin ⁡ ωt cos ⁡ ωt+ cos ⁡ ωt sin ⁡ ωt )=0 so v ⊥r

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

Solution

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