the correct answer is d
Explanation:
The laws of mechanics are related
F = m a
the acceleration of the body is given by the kinematics
substituting
a = \frac{d2x}{dt^2}
Therefore, in order to obtain the force (interaction of a body), continuous curves are needed and derivable from the position and the speed, for which all change in the trajectory of a body must be smooth where smooth is understood to have until the second derived.
Consequently the correct answer is d