No in fact vacuum motors are great for many many things;
just not exactly anything that's unplugged.
you can build a nice vacuum former with that and a table grill,
you can make your own smallish A/C device to chill on a hot day...
you can make much more than I can even think of I'd say;
but a goKart isn't exactly the first thing I'd try with a 'potentially' AC only motor in my hands.
I don't say it's impossible..
In fact I'm nearly 100% sure it IS possible to power a gokart with the full force of a vac or washing machine motor or anything that provides enough power.
The thing is: it's an extremely steep learning curve to get it done,
and if you don't know how to do it yourself, it's nearly impossible to teach you over the internet.
You'd need to custom build a controller, that in itself is something that even people with a masters degree in electronic engineering will fail the first couple of times.
it'll be a year until you can first bench test the motor/controller unit...
by that time you could have found a more powerfull DC motor incl a controller for less than you spend trying...
So, I'm sorry,
but either you know exactly what you're doing here or you should just find something else to power your kart with.
'sid