The position vector of the particle is r t = a cos ⁡ ω t i ^ + a sin ⁡ ω t j ^ , where a and ω are real constants of suitable dimensions. The acceleration is

Step-by-step solution

Given that, r t = a cos ⁡ ω t i ^ + a sin ⁡ ω t j ^ ∵ v → = d r t d t = - a ω sin ⁡ ω t i ^ + a ω cos ⁡ ω t i ^ j a → = d v → d t = - a ω 2 cos ⁡ ω t i ^ - a ω 2 cos ⁡ ω t j ^ a → . v → = a 2 ω 3 sin ⁡ ω t cos ⁡ ω t - a 2 ω 3 sin ⁡ ω t cos ⁡ ω t ⇒ a → . v → = 0 Above result implies that acceleration is perpendicular to velocity.