How are distance and speed related? If you know how fast someone is moving, can you determine how far they have traveled? Through the simulation on this page, you’ll explore how these two quantities are connected as they change over time.
Click “Play” to start the simulation! Watch the person’s motion and compare how their distance and speed change over time by observing the graphs.
This simulation provides a real-world example of the connection between integration and differentiation. To learn more about this relationship, visit the interactive learning resource on the Fundamental Theorem of Calculus.
Let’s Play a Game!
Through the simulation above, you’ve explored how distance and speed change over time. Now it’s time to put your understanding to the test with a game!
Take a look at the game panel. Your mission is simple:
Travel to Pole 1 and come to a stop there. Then set off again and stop at Pole 2.
Adjust the speed graph (shown in red) by dragging its control points. As you do, keep an eye on the distance graph as well. Ready? Click “Start”!