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If the acceleration of an object is given by dv/dt = −2v, Find the position function s(t) if v(0) = 7 and s(0) = 0.

User Jameila
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1 Answer

5 votes

Answer:

Explanation:

Given that acceleration of an object is


(dv)/(dt) =-2v\\(dv)/(v) =-2dt\\ln v = -2t+C\\

is the solution to the differential equation

Since v(0) =7

we get ln 7 = C

Hence
lnv = -2t+ln 7\\v=7e^(-2t)

since velocity is rate of change of distance s we have


v=(ds)/(dt) =7e^(-2t)\\s= [tex]s(t) =(-7)/(2) (e^(-2t))+C)[

substitute t=0 and s=0


C=7/2

So solution for distance is


s(t) =(-7)/(2) (e^(-2t)-1)

User Anaya
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