Wait..
the battery is overkill, and depending on the motor you'll end up using, you will need two or three or even four to provide the Voltage you need
(24V, 36V or 48V motors are common)
So 74Ah car battery is not a wise decision

just think about what four of them would weigh
If you want to go cheap, use motorbike batteries..
YB4-LB for example a small gel battery (5Ah 12x7x9 cm and roughly 1.7kg each ~$20)
again twice the cpacity I suggested (four times of what you need) and
four of them are lighter than just ONE car battery with 74Ah (about 16kg at least)
and just slightly more expensive.
Anyways..
yes, all dc motors can run backwards,
except for the few ones you didn't even think about (like a car starter motor)
Yes, there is a switch (it's called contactor)
but it's not what you think it is...
I have the feeling you have a wrong idea of how to build an electric motor driven kart

Forgive me if I'm mistaking..
but if at any point you thought about "resistor" or "potentiometer" to adjust the speed
you are wrong.
That's just not the way it works.
You need a controller for the motor.
Small motors like the one we are talking about don't need nothing fancy, a $30 dollar controller will do.
just no RC controller of course, but one off a e-scooter for example.
downside: the ones I can think of do not provide a reverse mode...
So maybe there's some research needed here
Anyways.. please take a look at the forums..
Jim-L-L for example just had his kid's kart converted to a 500W electric drive IIRC.
should be fairly easy to find.
Also there are numerous threads about electric motors, controllers and such,
just take a look at those for a better understanding of the concept.
'sid