When a vehicle slows down, its speed decreases. This is a deceleration. The resultant force needed is found from force = mass × acceleration, so the shorter the time it takes to stop, the larger the deceleration and the larger the force on everything in the vehicle.
In a crash a car can stop very quickly, in a tenth of a second or less. A 70 kg passenger decelerating at 200 m/s2 feels a force of 14000 N, which is about 20 times their weight of 700 N. Forces this large cause injury, such as broken bones, damage to organs, whiplash to the neck and head injuries.
Large decelerations are also dangerous when the driver brakes very hard. The large braking force can make the tyres skid so the driver loses control. The brakes also transfer a lot of kinetic energy to thermal energy very quickly and can overheat.
Safety features work by making the stopping time longer. Crumple zones, seat belts that stretch slightly, airbags and cycle helmets all spread the stop over more time, so the deceleration and the force on the person are smaller and there is less risk of injury.