🤓 Based on our data, we think this question is relevant for Professor Roland's class at NCSU.

The figure shows the velocity of a train as a function of time.

(a) At what time was its velocity greatest?

(b) During what periods, if any, was the velocity constant?

(c) During what periods, if any, was the acceleration constant?

(d) When was the magnitude of the acceleration greatest?

We're looking at a *velocity graph* to determine some things about the *velocity and acceleration* of at train.

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, and the slope of a velocity graph is the acceleration.

Velocity & Acceleration Graphs

Velocity & Acceleration Graphs

Velocity & Acceleration Graphs

Velocity & Acceleration Graphs