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Question Number 13751 by Nayon last updated on 23/May/17

$$\frac{ds}{dt}=v,\frac{dv}{dt}=a,\frac{da}{dt}=b,\frac{db}{dt}=e,\frac{de}{dt}=f$$$$\frac{df}{dt}=g,\frac{dg}{dt}=h,\frac{dh}{dt}=i,\frac{di}{dt}=j,\frac{dj}{dt}=k,.....$$$$nowifwecontinuethisprocessto$$$$infinity..andif{v}_0,v,a,b,e,f,g,h,i,$$$$j,................=1.thencalculate$$$$theformulaofvands...$$$$$$

Commented by ajfour last updated on 23/May/17

$$s=v={\mathit{e}}^{\mathit{t}}$$

Commented by Nayon last updated on 23/May/17

$$detAils$$

Commented by Nayon last updated on 23/May/17

$$v=e^{t}rightbut$$$$s=e^t-1$$$$$$

Commented by ajfour last updated on 23/May/17

$$agree$$

Answered by ajfour last updated on 23/May/17

$$s\left(t\right)=s\left(0\right)+{ts}^{\prime }\left(0\right)+\frac{t^2}{2!}{s}^{″}\left(0\right)+...$$$$andinquestion,$$$$s^{\prime }\left(0\right)=s^{″}\left(0\right)=....=1,s\left(0\right)=0$$$$so,s\left(t\right)=-1+(1+t+\frac{t^2}{2!}+....)$$$$s\left(t\right)=e^t-1$$$$v\left(t\right)=\frac{ds}{dt}=e^t.$$$$$$

Commented by Nayon last updated on 24/May/17

$$Hasthereanyobjectinthe$$$$universewhichadherethisformula?$$

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