Conservation of momentum, ignoring friction..., and doing some guess work, since I haven't done physics in a minute, and I don't feel like looking it up....
Average car is approx 4000lbs, travelling 65mph is an approx momentum of 260,000 lbs*mph. Average golf cart is approx 800-1000lbs, I'll use 1000. So, that translates to suddenly being propelled at 260 mph, if the car came to a full stop, which it wouldn't. It would only transfer some of it. I'll just use an estimate that the car would lose approx 1/4 of its momentum, and the cart would only receive 1/4. it would still propel the cart 65mph instantly, that's about 95 feet in 1 second. So, in 3-5 seconds, sure, 300 feet seems doable.