As an everyday example, driving in a car can show effects of acceleration and jerk. High-powered sports cars offer the feeling of being pressed into the cushioning, but this physics 1 for dummies pdf free the force of the acceleration. Only in the very first moments, when the torque of the engine grows with the rotational speed, the acceleration grows remarkably and a slight whiplash effect is noticeable in the neck, mostly masked by the jerk of gear switching.
A collision can do so to an even greater degree, not allowing for a tonicity controlled body at all. Every experienced driver knows how to start and how to stop braking with low jerk. This is a force opposing the increase in displacement. The drag coefficient depends on the scalable shape of the object and on the Reynolds number, which itself depends on the speed. Extrapolating from the idealized settings, the effect of jerk in real situations can be qualitatively described, explained and predicted. Dirac delta reconstructs exactly the jump discontinuity in the acceleration belonging to the Dirac delta in the jerk.
The whole path is continuous and its pieces are smooth. Dirac delta scaled with this value, for purely geometric reasons, when it passes the connection of the pieces. See below for a more concrete application. Let a mass, connected to an ideal spring, oscillate on a flat, idealized surface with friction. Therefore the acceleration jumps by this amount divided by the mass. This, of course, neglects all effects of tire sliding, dipping of suspension, real deflection of all ideally rigid mechanisms, etc. Another example of significant jerk, analogous to the first setting, is given by cutting the rope twirling a particle around a center.