Question Number 37972 by Rio Mike last updated on 20/Jun/18
$$\:{The}\:{distance}\:{S}\:{metres}\:{is}\: \\ $$$${given}\:{as}\:{a}\:{funtion}\: \\ $$$${f}\left({t}\right)\:{where}\:{is}\:{time}\:{taken}... \\ $$$${if}\:{S}\:=\:{t}^{\mathrm{3}} \:+\:{t}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$${find}\:{the}\:{velocity}\:{and}\:{acceleration} \\ $$
Answered by Joel579 last updated on 20/Jun/18
$${s}\left({t}\right)\:=\:{t}^{\mathrm{3}} \:+\:{t}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$${v}\left({t}\right)\:=\:\frac{{ds}}{{dt}}\:=\:\mathrm{3}{t}^{\mathrm{2}} \:+\:\mathrm{2}{t} \\ $$$${a}\left({t}\right)\:=\:\frac{{dv}}{{dt}}\:=\:\mathrm{6}{t} \\ $$