Biggest problem with taking pics of fast objects with point and shoot and most mirorrless cameras is the inability to focus quickly and even more so , ability to track focus points .
First off , don't even bother with anything other than a DSLR .
Reason is DSLRs generally use Phase Detection autofocus ( when not using live view ) . This is much faster than contrast detection of a DSLR . Lots of info on the net regarding the focus type
The delay in the time you press shutter release on typical P&S and even good mirorless vs a DSLR is very noticeable . This is obviously important for a fast moving car
Second issue with focus is the ability to track focus . If you have a camera that does not have full control of autofocus points and tracking it is easy to have camera have sharp focus on the car you don't want a pic of
Before you think you can just run smaller aperture ( larger F stop ) to ensure everything is in focus, keep in mind this drives down shutter speed which is not what you want in a fast moving object
Lots of info on Nikon / Canon autofocus modes . The long and short if it is this. With a camera such as a higher end Nikon you can choose the number of focus points and how you want them to track DYNAMICLY
Nikon calls this "Dynamic" Canon calls this "point expansion" . So you choose the exact focus point ( could be a athelete's body, a car etc ) and once focus is acquired it will track the object and always continually focus on the one object
This is awesome for sports if you want to focus only on one player. If you loose object the system "predicts" from its movement and tries to reacquire at that point ( 3-D tracking focus setting )
Focus Speed with different lenses
I would avoid older "screw drive" lens and go with lens that has focus motor built in . Nikon calls this SWM , Canon USM, Sigma HSM
You need a fast ( large max aperture ) not only because you want to shoot a low F stop to keep shutter speed up but focus speed is always more reliable and faster with the pro lenses
The reason for this is when you press shutter release, the camera acquires focus with the aperature wide open. 2.8 lenses lets in far more light to get a good reliable quick focus, especially in lower light .
Even if you are shooting at F11, the focus is done at largest aperture ( smallest F stop ) the lens has . It is stopped down right before shutter release . That is why most DSLRs have DOF preview button since what you see in viewfinder ( what focus system sees ) is wide open
Frame Rate
Having a camera body that has higher frame rate is very useful for fast moving objects . Essentially you can spray and pray there are keeps
This is why the awesome Nikon D800 is not often used for pro sports . It has a relatively slow max frame rate of 4fps . My old D700 does 8fps !
The Nikon pro sports camera does 11 fps
Camera choices
I'm not saying you need a D4 to shoot cars, just don't get hung up on only looking at the megapixels . The flagship Nikon D4 "only" does 16mp compared to their half the cost D800 that does 36mp
If you want to take pics of race cars just for this one race, rent some gear and be done with it
I know the Nikon bodies so my suggestion to you that if you want to actually invest in a good camera for cars / sports / landscapes etc then buy a D7100 ( if you want crop sensor ) or D610
The lD5300 / D3200 Nikons don't have the full control of the all the settings as the more expensive D7100 has
Your choice of lenses is limited for your application . I would go with a 70-200 2.8 VRI ( used ) or VRII version as your least expensive option .
Most pro photographers that do race cars buy lenses that are far more expensive than the 70-200
Don't bother with a super zoom all in one for race cars. I have Nikon 28-300 and 24-120 F4 , both of which are not cheap lenses . Image quality is great but focus speed is noticeably slower than my 24-70 and 70-200 ( for reasons noted above )