A particle moves with an initial velocity ${\upsilon }_0$ and retardation $\alpha \upsilon ,$ where $\upsilon$ is velocity at any instant t. Then:

The particle comes to rest at $t=\frac{1}{\alpha }.$

The particle continues to move for a long time span

The particle attains a velocity $\frac{1}{2}{\upsilon }_0$ at $t=\frac{1}{\alpha }.$

The particle will cover a total distance $\frac{{\upsilon }_0}{\alpha }$