position vector of a particle is given by \(\sf r = r_0(1-at)t\) , where t is the time and a as well as \(\sf r_0\) are constant. How much distance is covered by the particle in returning to the starting point?

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position vector of a particle is given by \(\sf r = r_0(1-at)t\) , where t is the time and a as well as \(\sf r_0\) are constant. How much distance is covered by the particle in returning to the starting point?

Physics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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suggest you start with a drawing, this is a parabola then you can use calculus or algebra. simply completing the square should answer this for you without too much effort.

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