Replacing a battery with a charged capacitor

[svbalasub]

Homework Statement

A Vbatt = 1.5 V battery stores Ubatt = 2.25 kJ of energy. I want to replace this battery with a charged capacitor that stores the same amount of energy and puts out the same voltage. That is, I want a capacitor such that UC = 2.25 kJ and VC = 1.5 V. What must the capacitance of such a capacitor be? What charge must this capacitor hold? Reasonable capacitors typically have a capacitance of at most one farad. Is this capacitor a reasonable replacement for the battery?

Homework Equations

U=1/2 CV^2

The Attempt at a Solution

 

[cepheid]

If you already have the equation for the energy stored in the capacitor, and you know U, and you know V, why can't you just use this equation to solve for C yourself?

One thing that I've heard is a problem with caps as energy sources is that they discharge too quickly, i.e. you get the energy all at once instead of a little bit at a time as needed.