As already said, it is actually easy..
here is how I do it:
1. set the focus... since I mainly use auto mode, I point the camera on the road where the car will be when I will take the pic and focus there
2. the car arrived, I point at it, a bit before the focus point
3. I start "following" it, keeping it in the center of the picture if possible
4. I shoot the pic and keep following the car for a while
A little tip, if possible, try to be sure the camera won't have too much vertical movement (for pics like mines for instance, where the car basically follow an orizontal line in front of you.. in any case, no movement on the axis perpendicular to the one the car is following)
That's it... here are some examples taken with shutter set somewhere around 1/80 (automatically set at that speed since I also let the camera judge most of the time)
This was a cloudy day.. in sunny days should be a joke: for the following ones, shutter speed was always 1/640, sometimes even more I think and I didn't even had to move the camera to obtain sharp pics
As for your two pics dingo, do you recall what shutter speed you got there with auto mode?
And the new one in sport mode, what speed did it set the shutter