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.

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?

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 Velocity-Time Graphs & Acceleration concept. You can view video lessons to learn Velocity-Time Graphs & Acceleration. Or if you need more Velocity-Time Graphs & Acceleration practice, you can also practice Velocity-Time Graphs & Acceleration practice problems.

What professor is this problem relevant for?

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