###### Answer: C. the one going horizontal

In mechanics the derivative of the position vs . time graph of an object is equal to the velocity of the object. In the International System of Units the position of the moving object is measured in meters relative to the origin while the time is measured in seconds.Placing position on the y-axis and time on the x-axis the slope of the curve is given by:

The velocity of an object is the rate of change of its position with respect to a frame of reference and is a function of time . Velocity is equivalent to a specification of an object’s speed and direction of motion (e.g. 60 km/h to the north). Velocity is a fundamental concept in kinematics the branch of classical mechanics that describes the motion of bodies.

The last expression is the second derivative of position (x) with respect to time . On the graph of a function the second derivative corresponds to the curvature or concavity of the graph . The graph of a function with a positive second derivative is upwardly concave while the graph of a function with a negative second derivative curves in the …

Motion graphs and derivatives – Wikipedia

Motion graphs and derivatives – Wikipedia

Motion graphs and derivatives – Wikipedia

Motion graphs and derivatives – Wikipedia

Technically velocity contains information about the direction (speed does not). The graph is for positive velocity meaning that the body’s position s(t) is increasing with time (the body is moving to the right along the s-axis). I think we need to clarify this issue about area below the graph and positive/negative velocity .

A spacetime diagram is a graphical illustration of the properties of space and time in the special theory of relativity.Spacetime diagrams allow a qualitative understanding of the corresponding phenomena like time dilation and…