Inclined Plane

Position versus Time

What is the relationship between the length of the position arrow and the time variable?



A) Circular : x² + y² = Constant
B) Elliptical : ax² + by² = Constant
C) Parabolic : y = ax² + bx + c
D) Hyperbolic (I) : xy = Constant
E) Hyperbolic (II) : ax² - by² = Constant


If this picture looks unfamiliar, it is only because you usually see the graph oriented with the time axis horizontal.

From the position as a function of time we can calculate the velocity of the sphere. To review how this is done see Calculus (from a Physicist's Perspective).

Watch the Position Arrow and the Velocity Arrow as the sphere moves on the incline.

What is the relationship between the Velocity Arrow and the Position Arrow? Notice that no coordinate directions or dimensions are given. The relationship sought is purely geometric.

A) The Velocity Arrow is parallel to the Position Arrow : same direction.
B) The Velocity Arrow is antiparallel to the Position Arrow : opposite direction.
C) The Velocity Arrow is perpendicular to the Position Arrow.
D) The Velocity Arrow is parallel to the (future) change in the Position Arrow.
E) The Velocity Arrow is antiparallel to the (future) change in the Position Arrow.


Just as with the position as a function of time display, we may place successive velocity arrows side by side. The resulting picture is a plot of the velocity arrow's length as a function of time.