Whiplash is a relatively common form of neck sprain that is caused by a hyper extension of the neck causing injury to the cervical, thoracic, or lumbar spines. Whiplash is most commonly caused by rapid movement of the head back and forward.
Arthur C Croft has stated that hyperextension of the neck is caused by an great acceleration of the body that your head can not keep up with. He uses the term Cervical Acceleration/deceleration or CAD as a short name for this injury. He studied the connection between the acceleration and the speed of impact of a vehicle and weather or not they sustained an injury. He found that above 6mph the victims seemed start to sustain injuries. See Figure 1 below
Figure 1 (Velocity-Acceleration plot of collisions)
He states that right before the injury happenings, the spine is bent into an S shape. See Figure 2 below for the progression of the spine taking on the s shape before the injury is incurred.
Figure 2 (S shape of the spine progression in a crash)
It is later stated that injuries to the neck start to occur at an impact speed of 3.7mph
To simplify things I will convert the impact speed of 3.7mph to about 6kmh to simplify the calculations. I will combine this with the average weight of a human head, which is about 5kg, and will try to calculate the force at which the neck is damaged. The one more piece of information I need is the time it takes for the head to decelerate completely so I can get the acceleration. Wikipedia states that the hypertension of the neck occurs after 100ms from point of impact, though this number is not cited it will be used for the simulation.
In the upcoming model I will note that an injury will occur if the person have a deceleration or acceleration of ones head more than 60km/s2.
Please see Figure 3 below for the model of a man on a motor cycle. Also see Equation 1 below for the mathematical representation of the system in Figure 3.
Figure 3 (model of a man on a motor cycle)