A differentiable position function satisfies x(t₁)=x(t₂), with t₂>t₁, and the particle is not at rest throughout the interval. Which statements are correct?
Select all that apply

Question

A differentiable position function satisfies x(t₁)=x(t₂), with t₂>t₁, and the particle is not at rest throughout the interval. Which statements are correct?

G1 Physics · Accepted Answer

Since x(t₂)=x(t₁), displacement is zero and average velocity is zero. Because the particle actually moves, total distance is positive, so average speed is positive. Also, by Rolle's theorem, for a differentiable x(t) with equal endpoint positions, there exists at least one instant c between t₁ and t₂ such that dx/dt=0. Thus all four statements are correct.