We are asked to find the **distance covered**** **given velocity-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, and the slope of a velocity graph is the acceleration.

To move left to right, we use the area under the curve—but remember, that area only tells us the *displacement* or the __change__ in *velocity*! To find a velocity, we take the area under an acceleration curve and **add the ****initial velocity**. To find a position, we'd take the area under a velocity curve and **add the ****initial position**.

This problem is a little odd for its type, because we only want the displacement and not the final position. (Here, displacement is equal to distance traveled: since *v* ≥ 0 everywhere on the graph, the runner's velocity is always in the positive *x*-direction.)

How far does the runner whose velocity-time graph is shown in the figure travel in 16 s? The vertical scaling is set by *v*_{s}= 8.0 m/s.

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

What professor is this problem relevant for?

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

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.