Question Number 155643 by zen17 last updated on 03/Oct/21
Commented by yeti123 last updated on 03/Oct/21
$${s}\:=\:\frac{\mathrm{1}}{\mathrm{6}}{t}^{\mathrm{4}} \:−\:\frac{\mathrm{7}}{\mathrm{6}}{t}^{\mathrm{3}} \:−\:\mathrm{7}{t}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{2}}{t}\:+\:\mathrm{1} \\ $$$${v}\:=\:\frac{{ds}}{{dt}}\:=\:\frac{\mathrm{4}}{\mathrm{6}}{t}^{\mathrm{3}} \:−\:\frac{\mathrm{21}}{\mathrm{6}}{t}^{\mathrm{2}} \:−\:\mathrm{14}{t}\:+\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{{dv}}{{dt}}\:=\:{a} \\ $$$$\frac{\mathrm{12}}{\mathrm{6}}{t}^{\mathrm{2}} \:−\:\frac{\mathrm{42}}{\mathrm{6}}{t}\:−\:\mathrm{14}\:=\:\mathrm{1} \\ $$$$\mathrm{2}{t}^{\mathrm{2}} \:−\:\mathrm{7}{t}\:−\:\mathrm{15}\:=\:\mathrm{0} \\ $$$${t}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{46}} \\ $$$${v}\:\overset{{t}=\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{46}}} {=}\frac{\mathrm{4}}{\mathrm{6}}\left(\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{46}}\right)\:−\:\frac{\mathrm{21}}{\mathrm{6}}\left(\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{46}}\right)\:−\:\mathrm{14}\left(\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{46}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$