Question Number 207901 by Tawa11 last updated on 29/May/24
Answered by mr W last updated on 30/May/24
$$\boldsymbol{{v}}=\frac{{d}\boldsymbol{{r}}}{{dt}}={e}^{{t}} \left(\mathrm{cos}\:{t}−\mathrm{sin}\:{t}\right)\:\boldsymbol{{i}}+{e}^{{t}} \left(\mathrm{sin}\:{t}+\:\mathrm{cos}\:{t}\right)\:\boldsymbol{{j}} \\ $$$$\boldsymbol{{a}}=\frac{{d}\boldsymbol{{v}}}{{dt}}=−\mathrm{2}{e}^{{t}} \:\mathrm{sin}\:{t}\:\boldsymbol{{i}}+\mathrm{2}{e}^{{t}} \:\mathrm{cos}\:{t}\:\boldsymbol{{j}} \\ $$$$\mid\boldsymbol{{a}}\mid=\sqrt{\left(−\mathrm{2}{e}^{{t}} \:\mathrm{cos}\:{t}\right)^{\mathrm{2}} +\left(\mathrm{2}{e}^{{t}} \:\mathrm{sin}\:{t}\right)^{\mathrm{2}} }=\mathrm{2}{e}^{{t}} \\ $$
Commented by Tawa11 last updated on 30/May/24
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate} \\ $$