 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-2/5c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

A particle released at the origin at time

s

satisfies

\overset{x}{˙} = 2 t, \overset{y}{˙} = x t, x (s) = y (s) = 0.

Integration gives

x (t) = t^{2} - s^{2}, y (t) = \frac{( t ^{2} - s ^{2} ) ^{2}}{4} .

Its distance from the origin is therefore

x^{2} + y^{2} = (t^{2} - s^{2}) 1 + \frac{( t ^{2} - s ^{2} ) ^{2}}{16} .

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