This problem asks us to describe the **direction** and **relative magnitude** of the object's velocity at various points **based on its position-time graph**.

Anytime we're given a **position**, **velocity**, or **acceleration** graph to work with, a PVA diagram like the one below can help remind you of the relationships between the three functions.

$\mathit{P}\begin{array}{c}{\mathbf{\leftarrow}}\\ {\mathbf{\to}}\end{array}\underset{{\mathit{s}}{\mathit{l}}{\mathit{o}}{\mathit{p}}{\mathit{e}}}{\overset{{\mathit{a}}{\mathit{r}}{\mathit{e}}{\mathit{a}}}{\mathit{V}}}\begin{array}{c}{\mathbf{\leftarrow}}\\ {\mathbf{\to}}\end{array}\mathit{A}$

Moving left to right, we take the slope of the graph—the slope of a position graph is the velocity.

Horizontal lines have zero displacements (Δx) and zero slopes. The diagram below demonstrates how magnitude of a slope varies.

**(a) **We're asked to determine at which point the object is moving the **slowest.**

The figure below shows the position-versus-time graph for a moving object. At which lettered point(s):**(a)** Is the object *moving* the slowest?**(b)** Is the object moving the fastest?**(c)** Is the object at rest?**(d)** Is the object moving to the left?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Position-Time Graphs & Velocity concept. You can view video lessons to learn Position-Time Graphs & Velocity. Or if you need more Position-Time Graphs & Velocity practice, you can also practice Position-Time Graphs & Velocity practice problems.