For the element shown below, v(t)=1/2tVolts and i(t) = 12t-4t^2 Amps.
(a) Find the instantaneous power p(t) as a function of time.
+ v(t) -
|------|
-----| |-----
|------|
i(t)----->
Power where? Delivered to the capacitor? You don't show a resistor. Your circuit seems to have been lost in translation to the figure shown.
Is this an AC circuit or is v(t) a general function?