Question Number 14219 by tawa tawa last updated on 29/May/17
Answered by ajfour last updated on 29/May/17
$$\:\:\:\:\:\:\:\:\:\:\:\:\bar {{s}}=\mathrm{4}{t}^{\mathrm{3}} \hat {{i}}−\mathrm{2}{t}^{\mathrm{2}} \hat {{j}}+\mathrm{3}{t}\hat {{k}}\:\:\:..\left({i}\right) \\ $$$$\left({a}\right)\:\bar {{v}}=\frac{{d}\bar {{s}}}{{dt}}=\mathrm{12}{t}^{\mathrm{2}} \hat {{i}}−\mathrm{4}{t}\hat {{j}}+\mathrm{3}\hat {{k}}\:\:\:...\left({ii}\right) \\ $$$$\left({b}\right)\:{speed}\:{at}\:{t}=\mathrm{1}{s} \\ $$$$\:\:\:=\mid\bar {{v}}\mid_{{t}=\mathrm{1}{s}} =\sqrt{\mathrm{144}+\mathrm{16}+\mathrm{9}}\:=\mathrm{13} \\ $$$$\left({c}\right)\:\:\bar {{a}}=\frac{{d}\bar {{v}}}{{dt}}=\mathrm{24}{t}\hat {{i}}−\mathrm{4}\hat {{j}}\:\:\:\:\:\:\:.....\left({iii}\right) \\ $$$${at}\:{t}=\mathrm{3}{s},\:\:\bar {{a}}=\mathrm{72}\hat {{i}}−\mathrm{4}\hat {{j}} \\ $$$$\left({d}\right)\:{at}\:{t}=\mathrm{0},\:\:{from}\:{eqn}\:\left({ii}\right): \\ $$$$\:\:\:\:\:\bar {{v}}_{\mathrm{0}} =\mathrm{3}\hat {{k}}\:\:\:.\: \\ $$
Commented by tawa tawa last updated on 29/May/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{effort}. \\ $$