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Help solving this Calculus problem!?
ds/dt = sqrt(2gs) where g is a constant
Find s as a function of t
A step by step solution would be wonderful!
2 Answers
- xyzzyLv 77 years agoFavorite Answer
ds/sqrt(2gs) = dt
david, you dropped a sign
(2g)^(-1/2) [(s)^(-1/2) ds] = dt <<< integrate
(2g)^(-1/2) (s)^(1/2) / (1/2) + C = t << reflexive prop
t = (2)[(2g)^(-1/2) (s)^(1/2)] + C
(t + c) = 2(2g)^-1/2s^1/2
2s/g = (t + c)^2
s = g/2 (t+c)^2
or
s = (sqrt(g/2) t +c)^2
- davidLv 77 years ago
ds/dt = sqrt(2gs) separate variables --- s and ds to left, t and dt to right
ds/sqrt(2gs) = dt
(2g)^(1/2) [(s)^(1/2) ds] = dt <<< integrate
(2g)^(1/2) (s)^(3/2) / (3/2) + C = t << reflexive prop
t = (2/3)[(2g)^(1/2) (s)^(3/2)] + C << answer