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.

Answer 1

Let $x$ be the distance traveled by the particle in time $t$.

Now, its velocity is given by $\frac{dx}{dt}$ and acceleration is given by $\frac{d^{2}x}{d{t}^2}$.

According to the problem,

$\frac{d^{2}x}{d{t}^2}=\frac{dx}{dt}$.

This is the required differential equation.