A problem with using a camera in a high vibration environment, like a race car is... the vibration. Unless you can get it to remain perfectly still in relation to the object of the video, it will be very blurry and you may not get any meaningful data.
A camera with image stabilization will be ideal. An action camera with image stabilization would be best since the design specifications will be the closest to that required for use in a race car. They are designed to be mounted to things which makes positioning pretty easy. Some are remote controlled so you tell it to start and stop recording remotely.
Lawrenceville, GA