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Question Number 99962 by Rio Michael last updated on 24/Jun/20

$$\mathrm{A}\mathrm{particle}Q\mathrm{moves}\mathrm{in}\mathrm{a}\mathrm{plane}\mathrm{and}\mathrm{its}\mathrm{polar}\mathrm{coordinate}(r,\theta )$$$$\mathrm{are}\mathrm{described}\mathrm{by}r={at}^2\mathrm{and}\theta =\frac{1}{3}{t}^4\mathrm{find}\mathrm{its}$$$$\mathrm{speed}\mathrm{at}t=2\mathrm{s}$$

Answered by smridha last updated on 24/Jun/20

$$\overrightarrow{\mathit{v}}=\stackrel{\bullet }{\mathit{r}}\hat{r}+\mathit{r}\stackrel{\bullet }{\mathit{\theta }}\hat{\mathit{\theta }}=2\mathit{a}\mathit{t}\hat{\mathit{r}}+\frac{4}{3}{\mathit{a}\mathit{t}}^5\hat{\mathit{\theta }}$$$$\overrightarrow{\mathit{v}}={\left[\frac{d\overrightarrow{\mathit{r}}}{dt}\right]}_{t=2}=4\mathit{a}\hat{\mathit{r}}+\frac{128}{3}\mathit{a}\hat{\mathit{\theta }}$$

Commented by Rio Michael last updated on 24/Jun/20

$$\mathrm{thank}\mathrm{your}\mathrm{sir}.$$

Commented by smridha last updated on 24/Jun/20

$$\mathit{w}\mathit{e}\mathit{l}\mathit{c}\mathit{o}\mathit{m}\mathit{e}$$

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