I had an old man rear-end me at a stop light. He wasn't going too fast to stop. He just never even tried to apply the brake. Fortunately, nobody was hurt. He tried to convince me not to report the accident, so I assume that sort of thing happened to him several times.
Not a week goes by without a story about an old person failing to brake (or accelerating instead of braking) before crashing into a coffee shop, daycare center, street festival, etc. It's a serious problem.