A differentiable function x(t) satisfies x(t₁)=x(t₂), t₂>t₁, and the particle actually moves during the interval. Which statements are correct?
Select all that apply

Question

A differentiable function x(t) satisfies x(t₁)=x(t₂), t₂>t₁, and the particle actually moves during the interval. Which statements are correct?

G1 Physics · Accepted Answer

Equal endpoint positions imply zero displacement, hence average velocity is zero. Since the particle actually moves, total distance and average speed are positive. By Rolle's theorem, because x(t) is differentiable and x(t₁)=x(t₂), at least one instant c exists with dx/dt=0. Thus all statements are correct.