Physics - NLM Question with Solution | TestHub

$\mathrm{F}={\mathrm{F}}_0{\mathrm{e}}^{-\mathrm{bt}}$ $\Rightarrow \mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}=\frac{{\mathrm{F}}_0}{\mathrm{m}}{\mathrm{e}}^{-\mathrm{bt}}$ $\Rightarrow \frac{\mathrm{dv}}{\mathrm{dt}}=\frac{{\mathrm{F}}_0}{\mathrm{m}}{\mathrm{e}}^{-\mathrm{bt}}$ $\int \mathrm{dv}={\int }_0^{\mathrm{t}}\frac{\mathrm{F}}{\mathrm{m}}{\mathrm{e}}^{-\mathrm{bt}}\mathrm{dt}$ $\Rightarrow v=\frac{F}{m}\left[\frac{-1}{b}\right]{\left[e^{-bt}\right]}_0^t$ $\Rightarrow v=\frac{F}{mb}\left[e^{-bt}\right]$ $v=0\text{ at }t=0$ and $v\to \frac{F}{mb}$ as $t\to \infty$ So, velocity increases continuously and attains a maximum value of $v=\frac{F}{mb}$ as $t\to \infty$.