A particle moves such that its position vector is r = a cos(ωt) $\hat{i}$ + a sin(ωt) $\hat{j}$ , where ω is constant. Which statement is true?
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Question

A particle moves such that its position vector is r = a cos(ωt) i ^ \hat{i} i ^ + a sin(ωt) j ^ \hat{j} j ^ ​ , where ω is constant. Which statement is true?

G1 Physics · Accepted Answer

Step 1: v=dr/dt=-aωsin(ωt)i+aωcos(ωt)j, so r·v=0 and v is perpendicular to r. Step 2: a=dv/dt=-aω²cos(ωt)i-aω²sin(ωt)j = -ω²r. Step 3: Thus acceleration points toward the origin. Final answer: B.

A particle moves such that its position vector is r = a cos(ωt) i ^ \hat{i} i ^ + a sin(ωt) j ^ \hat{j} j ^ ​ , where ω is constant. Which statement is true?

A particle moves such that its position vector is r = a cos(ωt) i ^ \hat{i} i ^ + a sin(ωt) j ^ \hat{j} j ^ , where ω is constant. Which statement is true?