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202403041703 Revision Paper II Q10

A body travels in a straight line but its speed at any time does not exceed 5\,\mathrm{m\,s^{-1}}. If it accelerates and decelerates at 2\,\mathrm{m\,s^{-2}}, find the shortest time needed to cover a distance of 30\,\mathrm{m} from rest to rest.

Extracted from A. Godman & J. F. Talbert. (1973). Additional Mathematics Pure and Applied in SI Units.

Roughwork.

For avoidance of physics is one by mathematical formulation.


\begin{aligned} v & = u+at \\ 5 & = 0 + 2t_1 \\ \textrm{Eq. (1):}\qquad\qquad t_1 & = 2.5\,\mathrm{s} \\ & \\ v & = u+at \\ 0 & = 5-2(t_3-t_2) \\ \textrm{Eq. (2):}\qquad t_3-t_2 & = 2.5\,\mathrm{s} \\ & \\ s & = \frac{((t_2-t_1)+(t_3-0))(v_{\textrm{max}})}{2} \\ 30 & = \frac{(t_2-2.5+t_3)(5)}{2} \\ \textrm{Eq. (3):}\qquad t_2+t_3 & = 14.5\,\mathrm{s} \\ \end{aligned}

What is t_3 then, in unit \textrm{sec}?

This problem is not to be attempted.