The UM-StL Anyspeed Applet
on 1-D Constant Acceleration

puzzler overview For more on the variables here, see this slide, this PDF, or

. A more recent javascript version of this calculator may be found here. Even newer, a Live3D platform for empirical studies of spacetime. Related notes: anyspeed modeling, metric-smart mechanics, and one-map two-clocks You might also enjoy some of our nanoexploration and information physics tools.

[Overview] [Examples] [Solve!] [Links]

You can solve most any unidirectional constant acceleration problem with this applet. At present, all distances are in lightyears [ly] and times in years [y]. Hence velocities are in units of lightyears per year, and accelerations are pretty much in "gees", since 9.8 [m/s^2] is about 1.03 [ly/y^2]. Convert the three independent variable (i.e. input) values that you have into these units before beginning.

The calculating engine accepts as it's 3 inputs only: [i] the frame-invariant "felt" or proper acceleration (i.e. traveler lightyears per square traveler year), [ii] one of the duration increments (e.g. map-years elapsed, traveler-years elapsed, or map-distance traveled), and [iii] the initial velocity (e.g. in map lightyears per year, or map lightyears per traveler year). To find out how these quantities relate, see the worked example here, and our 1D and map-based anyspeed-motion resource pages for more.

If different independent variable values are given, then you can iterate toward the solution you desire by playing with these quantities. Opportunities for being creative in some places also lie hidden. For example, inputting a negative elapsed-time means that the specified initial-velocity is really the final one.

By way of example...

Ask the calculator where you'll be if YOU accelerate uniformly at one "gee" from rest for 14.51 "traveler" years. Do this by pressing [ReSet] to make sure that proper-acceleration is set to 1 [tly/ty^2] or about a "gee", and that initial velocity is zero. Then type in "14.51" [ty] in the text box under [traveler-time elapsed], and hit [return] on your keyboard. I think that the answer is impressive. Considering that the Andromeda galaxy is only 2 million lightyears away, you will be half way there! If you wonder how this approach to anyspeed motion can be used to vaccinate students against Newtonian misconceptions in introductory physics, check out the 3rd of our abstracts to the Winter 1998 AAPT conference, and papers linked thereto.

Now that we have this solver up and running, we will enable other input combinations as opportunity permits, and perhaps offer a choice of units.

You may also look for an xtv plot of variable values in the near future (cf. image & beta of a version with the universal plot).

Caution: This applet requires a Java Development Kit 1.1 compatible browser. One reason is that version 1.1 of Java allows much cooler stuff to be done, even though the applet as written doesn't take advantage of it yet. The only browser I know of which supports JDK1.1 today is HotJava, available free from Sun if you register as a Java developer, but both Netscape and Internet Explorer are expected to offer compatible browsers soon. Here is what the applet looks like in a compatible browser. In the meantime, our non-Java solver (which accepts all Galilean-kinematic input combinations, in meters and seconds) should work for most anyone.