Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 170411 by Mastermind last updated on 23/May/22

The position of a body at time t (in  seconds) is given by s=t^3 −4, what is  the velocity and acceleration of the  object at time t=5 ?    Mastermind

$${The}\:{position}\:{of}\:{a}\:{body}\:{at}\:{time}\:{t}\:\left({in}\right. \\ $$$$\left.{seconds}\right)\:{is}\:{given}\:{by}\:{s}={t}^{\mathrm{3}} −\mathrm{4},\:{what}\:{is} \\ $$$${the}\:{velocity}\:{and}\:{acceleration}\:{of}\:{the} \\ $$$${object}\:{at}\:{time}\:{t}=\mathrm{5}\:? \\ $$$$ \\ $$$${Mastermind} \\ $$

Answered by alephzero last updated on 23/May/22

velocity = (ds/dt)  acceleration = (d^2 s/dt^2 )  (ds/dt) = ((d(t^3 −4))/dt) = ((d(t^3 ))/dt)−((d(4))/dt) =  = 3t^2 −0 = 3t^2   (d^2 s/dt^2 ) = ((d((ds/dt)))/dt) = ((d(3t^2 ))/dt) = 3((d(t^2 ))/dt) = 3×2t  = 6t  velocity at time 5 = (ds/dt)∣_5  = 3(5)^2  =  = 3×25 = 75  acceleration at time 5 = (d^2 s/dt^2 )∣_5  = 6×5  = 30

$$\mathrm{velocity}\:=\:\frac{{ds}}{{dt}} \\ $$$$\mathrm{acceleration}\:=\:\frac{{d}^{\mathrm{2}} {s}}{{dt}^{\mathrm{2}} } \\ $$$$\frac{{ds}}{{dt}}\:=\:\frac{{d}\left({t}^{\mathrm{3}} −\mathrm{4}\right)}{{dt}}\:=\:\frac{{d}\left({t}^{\mathrm{3}} \right)}{{dt}}−\frac{{d}\left(\mathrm{4}\right)}{{dt}}\:= \\ $$$$=\:\mathrm{3}{t}^{\mathrm{2}} −\mathrm{0}\:=\:\mathrm{3}{t}^{\mathrm{2}} \\ $$$$\frac{{d}^{\mathrm{2}} {s}}{{dt}^{\mathrm{2}} }\:=\:\frac{{d}\left(\frac{{ds}}{{dt}}\right)}{{dt}}\:=\:\frac{{d}\left(\mathrm{3}{t}^{\mathrm{2}} \right)}{{dt}}\:=\:\mathrm{3}\frac{{d}\left({t}^{\mathrm{2}} \right)}{{dt}}\:=\:\mathrm{3}×\mathrm{2}{t} \\ $$$$=\:\mathrm{6}{t} \\ $$$$\mathrm{velocity}\:\mathrm{at}\:\mathrm{time}\:\mathrm{5}\:=\:\frac{{ds}}{{dt}}\mid_{\mathrm{5}} \:=\:\mathrm{3}\left(\mathrm{5}\right)^{\mathrm{2}} \:= \\ $$$$=\:\mathrm{3}×\mathrm{25}\:=\:\mathrm{75} \\ $$$$\mathrm{acceleration}\:\mathrm{at}\:\mathrm{time}\:\mathrm{5}\:=\:\frac{{d}^{\mathrm{2}} {s}}{{dt}^{\mathrm{2}} }\mid_{\mathrm{5}} \:=\:\mathrm{6}×\mathrm{5} \\ $$$$=\:\mathrm{30} \\ $$

Commented by Mastermind last updated on 24/May/22

Thanks

$${Thanks} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com