This is a series of interactive pages on distance-time graphs. It is like having a motion sensor when you don't have a motion sensor.

Take Your Dog for a Walk
A clever interactive introduction to rate via distance-time graphs. The full-screen version would be useful if this is done as a whole class activity.
http://nrich.maths.org/public/viewer.php?obj_id=4803

Motion Capture
Motion capture is a similar program but graphs displacement rather than distance, so it may be useful to introduce the concept of first and second derivatives.
http://nrich.maths.org/public/viewer.php?obj_id=4873&part=

Motion Sensor
Motion Sensor tests for understanding - can you describe how a graph was made?
http://nrich.maths.org/public/viewer.php?obj_id=4872&part=

Steady Free Fall
In this rich activity, you drop a ball onto a ramp of your own design and see the graph of vertical distance versus time. Some challenging questions are asked.
http://nrich.maths.org/public/viewer.php?obj_id=4851&part=

From Sean Bird's website: "Put this [TI-Nspire] file in MyLib so that you can access the area approximation methods from any document."
The program will find the approximate areas for the left, right and midpt Reimann sums, as well as the trapezoid, Simpsons and numeric integral areas.
http://cs3.covenantchristian.org/bird/TTT/NspireCalc/area.tns

For other TI-Nspire files from Sean's website, visit:
http://cs3.covenantchristian.org/bird/Nspire.html

Cubic splines are cubic functions which are used in applications such as automobile design. The basic idea is to fit cubic polynomials between two neighboring data points while ensuring that there are "smooth" first and second derivatives at the data points. The program available from this website as a zip file is a useful tool for investigating cubic splines.
http://www.vias.org/simulations/simusoft_spline.html

Distance, time and velocity are an ideal means to understand the concept of derivation. By reducing the time interval until it becomes zero, the average velocity approaches the instantaneos velocity, which is equal to the first derivative of the distance (with respect to time). This is available as a zip file that can be downloaded.
http://www.vias.org/simulations/simusoft_difftangent.html

Choose a function and see the effect on the Riemann sum when you change the slice width. The file itself can be downloaded and installed on your computer or network.
http://www.vias.org/simulations/simusoft_riemannsum.html

Drop the ball in a vacuum under the influence of gravity. Set the green line to start the timer and the red line to stop the timer. From the time taken, estimate the average velocity over this time interval. Bonus: You can also choose your planet!
http://jersey.uoregon.edu/AverageVelocity/

This is a really cool interactive applet for demonstrating Newton's Method.
http://www.math.umn.edu/~garrett/qy/Newton.html

And here is one from the same website that shows a 'pathelogical' case, where the iterations don't converge on the nearest solution:
http://www.math.umn.edu/~garrett/qy/BadNewton.html

And here are six animated gifs that illustrate Newton's Method. Not interactive, but very nice nonetheless:
http://math.fullerton.edu/mathews/a2001/Animations/RootFinding/NewtonMet...

The above animations are part of a website that shows animations of a variety of iterative methods of finding zeros:
http://math.fullerton.edu/mathews/a2001/Animations/RootFinding/RootFindi...

This animation from Lou Talman is a dynamic representation of the area function we introduce in the standard proof of the Fundamental Theorem of Calculus.
http://clem.mscd.edu/~talmanl/HTML/FTOC.html

Type in your function and this clever TI-Nspire program will find the derivative and show all of the setting out. Marvellous!

Define the function f(1). Then use trap(b,a,n) to find the area under the function between a and b with n divisions using the trapezoidal rule. The function lrs(b,a,n) uses the lefthand rule, rrs(b,a,n) uses the righthand rule and sr(b,a,n) uses Simpson's Rule. How cool is that!