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The-distance-S-metres-is-given-as-a-funtion-f-t-where-is-time-taken-if-S-t-3-t-2-4-find-the-velocity-and-acceleration-

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

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