1.4 Graphing Motion

Position vs. Time Graphs

A position vs. time graph consists of an object's position graphed against time. Using the equation ${v_x=\frac{dx}{dt}}$, it can be derived that the slope of a tangent line at any point along the graph will show the velocity of the object at that time. Also, since acceleration is the derivative of the velocity with respect to time, we can plug in the definition of velocity to get that ${a_x=\frac{d^2x}{dt^2}}$. This means that the concavity of a position vs. time graph will correlate to the acceleration of the object at that time.