Question

The primary reason for the path of motion of an object being a smooth curve is: Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a the third derivative of parabolas is always zero. b inertia. c tangent direction unit vectors change continuously. d calculus must have continuous derivatives to apply correctly.

Answer 1

Answer:

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

         a = $\frac{dv}{dt}$

         v = $\frac{dx}{dt}$

         

substituting

         a = \frac{d2x}{dt^2}

         F = m $\frac{d^2x}{dt^2}$

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