Answer:
Acceleration,
\[\text{a}\,\text{=}\frac{dv}{dt}=-\text{r}{{\omega }^{\text{2}}}\text{sin}\omega
\text{t}\]or d\[dv=-\text{r}{{\omega }^{\text{2}}}\text{sin}\omega
\text{t}\,dt\]; Integrating it
we have \[\text{v}=-\text{r}\omega \left( -\frac{\cos
\omega t}{\omega } \right)=\text{ r}\omega \,\,\,\text{cos}\omega \text{t}\].
Now, velocity \[\text{v}=\frac{dx}{dt}=\text{ r}\omega
\text{ }\,\text{cos}\omega \text{t}\]or \[\text{dx }=\text{ r}\omega
\,\text{cos}\omega \text{t dt}\]
Integrating it, we have, \[\text{x}=\text{r}\omega \,\left(
\frac{\sin \omega t}{\omega } \right)=\text{r sin}\omega \text{t}\].
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