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Question Number 123767 by oustmuchiya@gmail.com last updated on 28/Nov/20

Answered by physicstutes last updated on 28/Nov/20

$$\mathbf{s}=2t+3\sin 2t$$$$\left(\mathrm{i}\right)\mathrm{Initiat}\mathrm{position}\mathrm{occurs}\mathrm{at}t=0\mathrm{s}$$$$\Rightarrow {\mathbf{s}}_0=2\left(0\right)+3\sin 2\left(0\right)$$$${\mathbf{s}}_0=0\mathrm{m}$$$$\left(\mathrm{ii}\right)\mathbf{v}=\frac{d\mathbf{s}}{dt}=2+6\cos 2t$$$$\mathbf{a}=\frac{d\mathbf{v}}{dt}=0-12\sin 2t$$$$\Rightarrow \mathbf{v}=(2+6\cos 2t)\mathrm{m}{\mathrm{s}}^{-1}\mathrm{and}\mathbf{a}=(-12\sin 2t)\mathrm{m}{\mathrm{s}}^{-2}$$$$\left(\mathrm{iii}\right)\mathrm{At}\mathrm{rest}\mathbf{v}=0$$$$\Rightarrow 2+6\cos 2t=0$$$$\cos 2t=-\frac{1}{3}$$$$2t=109.5\Rightarrow t=54.75\mathrm{s}$$$$\mathrm{b}.\mathrm{F}\left(x\right)=250e^{0.09x},x⩾0$$$$\frac{d\mathrm{F}\left(x\right)}{dx}=22.5e^{0.09x}$$$$\frac{d\mathrm{F}\left(x\right)}{dx}{\mid }_{8\mathrm{months}}=22.5e^{0.09\times 8}=46.2$$

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