During a rear-end collision, the passenger’s head initially at rest relative to the car seat tends to move backward when the car is suddenly accelerated forward. To minimise neck injury, engineers install padded headrests that stop the relative motion of the head within a permissible deceleration limit of 30 m s⁻². Assume the head acquires a relative speed of 4 m s⁻¹ with respect to the seat at the instant of collision and is then brought uniformly to rest by the padding.
(a) State which kind of inertia is involved in the initial motion of the passenger’s head.
(b) Calculate the minimum thickness of padding required so that the deceleration of the head does not exceed the specified limit.
(c) Explain how the provision of a properly designed headrest mitigates the risk of whiplash injuries in such collisions.