Well hi.. and

Yes you need a controller to run the motor.
allow me to ask: you said you're a mechanical engineer, and that tells me:
you MUST know the very basics of math already.
So the question I have is :
How is it possible that you cannot put your numbers in a preassembled and labeled formula?
And the most simple of them all... since the motor size is NOT negotiable,
all you need to know is how many batteries do you need to run it for 30 mins at least.
Your motor has 1000W (oh.. is that mechanical or electrical power?? HUUUGE DIFFERENCE)
anyways:
Watts are Amps times Volts
known is watts and volts..
1000W (electrical power) means a current of ~21 Amps
1000W (mechanical power) means ~1250W electrical power so a current of ~26Amps
So @ 48V you need 4 12V batteries with a useable energy of ~13Ah each to run the kart for half an hour.
The point is, what energy of the individual cell can be used and what remains unused (to keep the cell alive and/or the make the controller happy)
A good controller comes with a drop off voltage preset, generally that's ~90% of the nominal voltage.
your nominal voltage is 48 so the controller might shut down the motor as soon your batteries cannot provide more than 43.2Volts anymore
A fresh & fully charged 12V battery (as funny as it sounds) provides up to 14V (13.8V)
12.9V the very least...
If we now assume a cutoff at 41V that'd be each cell MUST provide 10.8V
And for a modern lead acid battery that means 90% of the cells capacity can be used
you need 13Ah at the very least means you need 4
good quality 12V cells bigger than 14.4Ah each.
based on the above assumptions.
Now, as soon as you have the motor and controller,
you can measure and calculate the real powerdraw and read the cutoff voltage from the manual
and then use these REAL numbers to find out what batteries you need.
personally I'd take the safe route and get a batpack twice as big just to make sure it holds up,
since batteries (especially lead acid ones) don't like a high current constantly drawn from them very much, and they tend to overheat and that drops the voltage by a good amount.
So get yourself 30AH batteries and you should be good for ~45mins
they're relatively cheap in lead acid (~45 USD) and not too heavy (~10-12kg)
so you spend less than 200$ and carry less than 50kg in batteries.
a LiFE bat pack would only weigh half of that;
but costs of ~100 USD per 10Ah 12V cell
would cause it to cost 1200 USD in the end. (five times as much)
'sid