As shown in the figure, wheel $\mathrm{A}$ of radius $r_{\mathrm{A}}=10\mathrm{ }\mathrm{c}\mathrm{m}$ is coupled by a belt $\mathrm{B}$ to the wheel $\mathrm{C}$ of radius $r_{\mathrm{C}}=25\mathrm{ }\mathrm{c}\mathrm{m}$. The angular speed of wheel $\mathrm{A}$ is increased from rest at a constant rate of $1.6\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d} {\mathrm{s}}^{-2}$. Time after which wheel $\mathrm{C}$ reaches a rotational speed of $100\mathrm{ }\mathrm{r}\mathrm{p}\mathrm{m}$, assuming the belt does not slip, is nearly