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তরঙ্গের

সমীকরণ $y=10 \sin \left(6 \pi t+\frac{\pi}{3}\right)$ হলে 3s এ এর বেগ ও ত্বরণ কত?

$\begin{array}{l}\quad y=10 \sin \left(6 \pi t+\frac{\pi}{3}\right) \\ \nu=\frac{d y}{d t}=10 \times 6 \pi \cos \left(6 \pi t+\frac{\pi}{3}\right) \\ \therefore \nu_{3}=\left.\frac{d y}{d t}\right|_{t=3}=94.248 \mathrm{~m} / \mathrm{s} \\ \text { Again, } a=\frac{d \nu}{d t}=-10 \times 6^{2} \pi^{2} \sin \left(6 \pi t+\frac{\pi}{3}\right) \\ \therefore a_{3}=\left.\frac{d \nu}{d t}\right|_{t=3}=-3077.0525 \mathrm{~m} / \mathrm{s}^{2}\end{array}$