A particle has position vector r = cos(ωt) x̂ + sin(ωt) ŷ, where ω is constant. Which statement is correct?

The velocity and acceleration are both perpendicular to r
The velocity and acceleration are both parallel to r
The velocity is perpendicular to r and the acceleration points toward the origin
The velocity is perpendicular to r and the acceleration points away from the origin

Correct answer: The velocity is perpendicular to r and the acceleration points toward the origin

Solution

r=(cos wt, sin wt). v=(-w sin wt, w cos wt) gives v.r=0, so velocity is perpendicular to r. a=(-w^2 cos wt, -w^2 sin wt)=-w^2 r, i.e. centripetal, pointing toward the origin (antiparallel to r), not perpendicular.

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