USAAAO — 2026 First Round

A planet moves in a circular orbit in a fixed plane with angular velocity ω, and let n-hat be a unit vector perpendicular to the orbital plane. Let the planet’s velocity vector as a function of time be given by v(t) = v₀(cos(ωt) i-hat + sin(ωt) j-hat). Define a(t) = dv/dt. Which of the following statements is correct? (Here, i-hat and j-hat are orthogonal unit vectors in the orbital plane.)