An object’s center of mass moves at a constant velocity y along a straight line past the origin. The accompanying figure shows the coordinate system and the line of motion. The dots show positions that are 1 sec apart. Why are the areas A₁, A₂, c, A₅ in the figure all equal? As in Kepler’s equal area law, the line that joins the object’s center of mass to the origin sweeps out equal areas in equal times.

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Kilometers 10 5 0 I " t = 6 t = 5 A5 A4 A3 5 A₂ K vAt A₁ 10 Kilometers vΔΙ = 2 = 15 1 > X