Find the position #s# as a function of time #t# from the given velocity #v= {ds}/{dt}#. Then evaluate the constant of integration so that #s=s_0# when #t=0#. #v=8(s)^(1/2), qquad s_0=9# Help please?? and thank you!!!

1 Answer
Ananda Dasgupta
May 13, 2018

#s(t)= (4t+3)^2#

Explanation:

For the given problem #v = {ds}/dt# becomes

#{ds}/dt = 8s^{1/2} implies#

#s^{-1/2}ds = 8dt implies#
(integrating)
#1/{1/2}s^{1/2} = 8t+2Cqquad implies sqrt s = 4t+C#
(in the first step we wrote the constant of integration as #2C# instead of #C# for convenience).

At #t=0#, #s = s_0 = 9#. This gives the constant #C# as

#sqrt 9 = 4times 0+Cqquad implies qquad C=3#

Hence

#sqrt{s} = 4t+3 implies#

#s = (4t+3)^2#

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