An insect crawls along the sides of a regular hexagon (Above, Right) with a uniform speed $$v$$ in the anticlockwise sense. Find the magnitude of its average velocity in moving from (i) A to C and (ii) A to D and (iii) A to E
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PLACEHOLDER ANSWER - the question has three answers. Let the side be $$s$$. (i) A to C covers $$2s$$ in time $$\frac{2s}{v}$$ with displacement $$AC = \sqrt{3}\,s$$, so the average velocity is $$\frac{\sqrt{3}}{2}v$$. (ii) A to D covers $$3s$$ with displacement $$2s$$, giving $$\frac{2}{3}v$$. (iii) A to E covers $$4s$$ with displacement $$\sqrt{3}\,s$$, giving $$\frac{\sqrt{3}}{4}v$$.