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

the correct answer is d

Step-by-step explanation:

The laws of mechanics are related

F = m a

the acceleration of the body is given by the kinematics

a =
`(dv)/(dt)`

v =
`(dx)/(dt)`

substituting

a = \frac{d2x}{dt^2}

F = m
`(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