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Solution
Please find below the solution to the asked query: 
$$\begin{gathered} \mathrm{Radius} \mathrm{of} \mathrm{circular} \mathrm{path}: \\ \mathrm{r}=\frac{\mathrm{D}}{2} \\ =\frac{105}{2} \\ =52.5 \mathrm{m} \\ \mathrm{Circumeference} \mathrm{of} \mathrm{circular} \mathrm{path}: \\ \mathrm{C}=2\mathrm{\pi r} \\ =2\mathrm{\pi }\times 52.5 \\ =329.9 \mathrm{m} \\ \mathrm{In} 5 \min , \mathrm{cyclist} \mathrm{covered} 1 \mathrm{round}. \\ \mathrm{So} \mathrm{in} 7 \min 30 \mathrm{s} \mathrm{it} \mathrm{covere} 1.5 \mathrm{round}. \\ \mathrm{Distance} \mathrm{travelled} \mathrm{in} 7 \min 30 \mathrm{s}: \\ {\mathrm{d}}_1=1.5 of circumference \\ =1.5\times 329.9 \\ =494.8 \mathrm{m} \\ \mathrm{After} 1.5 \mathrm{round} \mathrm{cyclist} \mathrm{with} 1 \mathrm{diameter} \mathrm{away} \mathrm{from} \mathrm{initial} \mathrm{position} \\ \mathrm{Displacement} \mathrm{in} 7 \min 30 \mathrm{s}: \\ {\mathrm{d}}_2=\mathrm{Diameter} \\ =105 \mathrm{m} \\ \mathrm{Speed}: \\ {\mathrm{v}}_1=\frac{{\mathrm{d}}_1}{\mathrm{t}} \\ = \frac{494.8}{7.5} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{65}\mathbf{.}\mathbf{9}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s} \\ \mathrm{Velocity}: \\ {\mathrm{v}}_2=\frac{{\mathrm{d}}_2}{\mathrm{t}} \\ = \frac{105}{7.5} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{14}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s} \end{gathered}$$
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