# calculus

a particle moves according to the law a=1/t √t. if s=8 when t=1. and s=16 when t=4. find v when t=9.

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1. do we have a = 1/(t√t) or is it a = (1/t)√t ??

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2. a = 1/(t√t)

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3. ok, then
a = t^(-3/2)
v = -2 t^(-1/2) + c

s = -4 t^(1/2) + ct + k

case1: s=8, when t = 1
8 = -4 + c + k
12 = c + k

case2: s = 16, when t = 4
16 = -4(2) + 4c + k
24 = 4c + k

subtract them:
12 = 3c
c = 4

back in 12 = c+k
12 = 4+k
k = 8

then v = -2/√t + 4
when t = 9
v = -2/3 + 4 = 10/3

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4. Thank you very, very much. I'm really grateful.

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5. welcome,

hope you checked my arithmetic

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