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Answer: \(\frac{d^2x}{dt^2} = k\frac{dx}{dt}\)

Let \(x\) be the displacement at time \(t\). Velocity \(= \frac{dx}{dt}\), acceleration \(= \frac{d^2x}{dt^2}\). Acceleration \(\propto\) velocity gives \(\frac{d^2x}{dt^2} = k\frac{dx}{dt}\), where \(k\) is a constant of proportionality.

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report
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