High RC Capacitors

Please explain more clearly. Do you want a charged capacitor to run a motor for 3 to 4 minutes? If so, what type of motor? What voltage and current are required to run it?

You require t = 180 [s]

We need to know more.

What is the expected "R" or "V" and "i" ?

What are the specifications of your DC motor?

For a ballpark estimate, one can use:

C [Farads] = i * t / deltaV

where { deltaV = Vstart-Vfinish } for the capacitor voltage.

I expect this will be a LARGE capacitor.