A particle moves so that its position vector is r = cos(ωt) î + sin(ωt) ĵ, where ω is constant. Which statement is true?
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A particle moves so that its position vector is r = cos(ωt) î + sin(ωt) ĵ, where ω is constant. Which statement is true?

G1 Physics · Accepted Answer

Step 1 — Principle: For sinusoidal vector motion, differentiate position to obtain velocity and acceleration. Step 2 — Working: Differentiate: v = -ωsin(ωt)î + ωcos(ωt)ĵ. Step 3 — Working: Since r·v = 0, velocity is perpendicular to position. Step 4 — Working: Further, a = -ω²r, so acceleration points towards the origin. Correct answer: A — Velocity is perpendicular to r and acceleration is directed towards the origin.