If you sit in a rolling car and the driver suddenly presses the break vs eases it in, you could halt with the same deceleration and yet one will feel smoother t

If you sit in a rolling car and the driver suddenly presses the break vs eases it in, you could halt with the same deceleration and yet one will feel smoother than the other. The car's position is not discontinuous, the velocity isn't either (in both cases it has to slow through intermediate velocities). It is the decelaration that in one case grows suddenly and in the other changes smoothly. On an egg, there is no place where curvature changes suddenly, and yet on a four point egg there are points where it does exactly that.