I think this product would be well served by alerting the user about car distance through some channel other than visual. When biking all visual attention should be focused forward, and the extra information sensed by this device could be delivered through some form of haptic feedback.
True, one option is to integrate haptic feedback into a sensor in the shoe. But even then, what action would one take based on this feedback. Should I stop, pedal faster or switch a lane. Just the radar feedback of 'something is about to hit you from behind' is probably not enough.
Activate a rear-mounted grenade launcher, of course. Well, in some of my violent daydreams regarding jerks in cars, at least.