Capacitor Bank Design for Electric Vehicle
There are multiple causes of improbability and impracticality, but they don't all reside in the amount of capacitance at a given voltage.

You can calculate how many volts and how many farads would be needed, and come up with a value which would work. The math is relatively simple as the energy, in ioules, is equal to 1/2 C V^2, where C is in farads and V is in volts. Believe it or not, but for a vehicle in the "e-bike" range, it isn't all that horrible for "e-bike" speeds, weights, and passengers. Many e-bikes are in the 300 to 600 watt motor range, and typically acceleration to full speed will happen within 10-15 seconds. On the high end, you'd need to store about 9,000 watt-seconds, or 9,000 joules.

Believe it or not, this isn't hard. I have a 90F supercap sitting on my desk. It happens to have a maximum working voltage of 5.6 volts, so four of them in series-parallel should make something capable of storing 90 farads at 10 volts. Plugging that into E = 1/2 C V^2 that's 9,000 watt-seconds. I really could get 600 watts out of that for 15 seconds.

[ I forgot to multiply by 0.5, so the answer is actually 4.5 kJ, not 9 kJ, but I hope my point is made ]

Except that you really can't. When that supercap is fully charged, 600 watts at 10 volts is 60 amperes, which is a VERY heavy wire. It is also impossible because a capacitor also has an "equivalent series resistance", and as you know, V = I * R. In this case, V is the voltage drop across the non-ideal-capacitor resistance (ESR), I is the current (60 amps), and R is the ESR value itself. There is also the non-small problem of getting 60 ampere through the small leads which are spot-welded onto the supercap. But more to the point, continuing to extract 600 watts as the voltage approaches zero requires an ever larger amount of current.

So, it isn't just a matter of finding a large enough supercapacitor -- for lower power applications, supercapacitors are more than up to the task. It's just that your specific application requires currents which are beyond the realm of reasonable possibility.