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A particular rocket is propelled such that its velocity increases as a function of time according to $v(t) = A t^\frac{1}{2}$, where $A$ is a constant.

Which of the following represents the correct acceleration function?

$a(t) = {\cfrac 2 3} A t^{3/2}$

$a(t) = 2 A t^{3/2}$

$a(t) = {\cfrac 1 2} A t^{-1/2}$

$a(t) = {\cfrac {-1} 2} A t^{-1/2}$

None of the above.