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Question
A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.
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Solution
Let S be the displacement of the particle at time 't'.
Its velocity and acceleration are `(dS)/dt and (d^2S)/dt^2` respectively.
Here `(d^2S)/dt^2 ∝ (dS)/dt`
⇒ `(d^2S)/dt^2 = k(dS)/dt`, ...(where k is constant ≠ 0)
This is the required differential equation.
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