Car vs. bicycle accidents typically result in serious injuries for the cyclist, even at low speeds. A cyclist who is wearing a helmet has more protection than one without, but it's also the only protection he or she has. The person in the car likely will not suffer any injuries, but the cyclist could be critically injured or even killed.
If this worries you, then you should also know that the roads have generally been getting more dangerous for cyclists in recent years. For instance, in a 2017 report, the U.S. Department of Transportation noted that 2016 saw 840 fatal cyclist accidents. That, the reports claimed, was the highest fatality total seen in more than two decades -- since 1991. It was also a 1.3% increase from 2015.