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

Question

A particle moves such that its position vector r → t = cos ⁡ ω t i ^ + sin ⁡ ω t j ^ where ω is a constant and t is time. Then which of the following statements is true for the velocity v → t and acceleration a → t of the particle:, v → is perpendicular to r → and a → is directed away from the origin, v → and a → both are perpendicular to r →, v → and a → both are parallel to r →, v → is perpendicular to r → and a → is directed towards the origin

MARKS App · Accepted Answer

r → = cos ⁡ ω t i ^ + sin ⁡ ω t j ^ v → = d r → d t = ω - sin ⁡ ω t i ^ + cos ⁡ ω t j ^ a → = d v → d t = - ω 2 cos ⁡ ω t i ^ + sin ⁡ ω t j ^ a → = - ω 2 r → ∴ a → is antiparallel to r → v → . r → = ω - sin ⁡ ω t cos ⁡ ω t + cos ⁡ ω t sin ⁡ ω t = 0 So v → ⊥ r →

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