UM-StL 1D Acceleration Solver

A browser-interactive resource for solving low and high speed constant acceleration problems.
Java and JavaScript (as of 6May2003) versions of this browser are now available on the web as well.

...But officer, I was only going 2 rb!...

What's New:
  • More on the variables used here: this PDF or this summary slide.
  • A Live3D platform for empirical studies of spacetime.
  • Equations and javascript calculator for a metric-based view of unidirectional motion.
  • Beginnings for a system of classroom-ready "web transparencies" on emerging science.
  • "Extreme Physics" motion simulator -- What patterns in nature do you detect?
  • A challenge for modelers who work from data, not interpretation!
  • Learn more about Hermann Minkowski & Ed Jaynes as a pioneers of deep simplification.
  • Consider participating in our interpretative cartooning festival.
  • "Teaching Newton with anticipation..." is our latest adaptation for intro physicists.
  • A vaccine to empower intro-students now AND minimize side-effects later!
  • One way to solve for everything in an anyspeed acceleration problem.
  • Three abstracts for the Winter 1998 AAPT Conference.
  • Find advice on almost any 1D constant acceleration problem here .
  • This is one leg of the UM-StL map-based anyspeed motion project.
  • Other pages include relativity rap, the andromeda problem, and some a1d-wuzzlers.
  • Cite/Link:
  • This release dated 14 Sep 1997 (Copyright by Phil Fraundorf 1988-1995)
  • At UM-StLouis see also: cme, infophys, phys&astr, programs, stei-lab, & wuzzlers.
  • Cartoon Credit: A c3p cartoon by John Lara, context-modified with permission.
  • Between summer '95 and July '96, the access log for this page shows 3393 visits.
  • Site page requests to jinx: 964/day in April 2005, to newton comparable, hence > 500,000/year.
  • Stat counter linked page requests since 4/7/2005: .

  • AnySpeed Engineering Complex ColorMath Information Physics NanoWorld Explorations Reciprocal World Silicon River StarDust in the Lab Web Puzzlers

    Do you want to skip down to explore a physics challenge, like guessing the time until you hit the water after jumping off a 50 foot bridge, estimating how many g's of acceleration you'll feel in accelerating a car from 0 to 60 mph in 8 seconds, or figuring the initial velocity of a speeding car which left 30 "meters of rubber" on the road in a 2 second screeching stop? If as with these challenges your problem involves acceleration which is constant (or nearly constant) in magnitude AND direction, you may find some guidance here. If what follows loses you entirely, see L. Gladney's Notes on Constant Acceleration at the University of Pennsylvania for a more fundamental primer on such challenges first.

    A novel feature of this page is that it also allows you to consider relativistic times and velocities, which make life more interesting as speeds approach that of light. For example, you might ask HOW FAR acceleration at one g for 50 years would take a traveler, assuming EITHER that the 50 years elapses on the clocks of an unaccelerated observer simply monitoring the expedition, OR that it elapses on the clocks of the accelerated traveler. Relativity has noticeable effects here: The two answers differ by nearly twenty powers of ten (cf. Lagoute & Davost 1995 in Am. J. Phys. 63, 221)! See also our Andromeda problem in "cold application testing" now.

    You have several choices on how to proceed at this point. One choice is to run these calculations on OUR computer through your web browser. This opportunity is provided below on this page, at least at those times when our query server is up and running. Another choice is to do the calculations on YOUR computer using MathCAD, or the MathSoft Browser available free here. For that purpose, we have set up 4 MathCAD worksheets, one for Newtonian or Low-Velocity Inputs, one for Relativistic Coordinate (Non-Accelerated Observer) Inputs, one for Traveler-Kinematic or Proper-Time/4-Velocity Inputs, and the last for Mixed-Kinematic Inputs. See below (and our relativity table of contents) for clues to what these things might mean. Thirdly, you may download a Visual BASIC program to do the calculations independently, from here. Lastly, you might want to try graphical solution of a problem. The picture below points to a page under development toward this goal.

    To run OUR query server, which for now solves relativistic problems exactly only from chase-plane (Galilean-kinematic) inputs, first decide WHICH of the 5 constant acceleration variables you already know. These variables are the acceleration itself (a0), the map-distance traveled (dx), the time elapsed (e.g. dt), and the initial/final velocities (e.g. v0/vf). You need to know three of them to solve a problem uniquely, as in these ordinary speed and relativistic examples.

    Our JAVA applet allows you to input the velocities and elapsed times in the (low-speed convenient) form used here, namely ``Galilean-kinematic'' velocity and ``chase-plane'' time. It also allows you to input instead the coordinate-velocity and elapsed map-time perceived by inertial observers of high-speed motion, OR the proper-velocity and elapsed proper-time reported to map-dwellers by the accelerated traveler. The differences between these variables (negligible at low speeds) are discussed in papers listed here, including physics/9611011 and physics/9704018. To keep separate all 3 kinematics while preserving the ``look'' of Galileo's original acceleration equations, we here use t and v for Galilean time and velocity, b and w for map-time and coordinate-velocity, and T (or tau) and u for the traveler's proper time and "spatial 4- velocity", respectively. Be cautious, since this notation changes with context from place to place. For example, our preference for high-speed applications is to use v and t for map-time and coordinate-velocity, tau and w for proper-time and proper-velocity, and something more obscure (like T and V) for the Galilean-kinematic variables of less interest at high speed.

    We often quote map-times in [years], traveler or proper-times in [tyears], coordinate-velocities in units of [c] (the speed of light in [lightyears/year]), and proper-velocities in [lightyears/tyear] or "roddenberries" [rb]. The latter name seems to have mnemonic value to students, perhaps via its mental connections to "hotrod" and the producer of the first Star Trek series (which like proper-velocity seems blissfully ignorant of the lightspeed limit to which coordinate-velocity is held). Deriving the inter-relationship between these parameters is simple (in html or postscript). Regardless of how you set up the problem, the inferred value of all 11 variables is provided in the Results Report.

    Note: These routines will work for solving constant acceleration problems in more than one spatial dimension, by simply ignoring that component of the velocity which is perpendicular to the direction of constant acceleration, if and only if that perpendicular velocity component is much less than the speed of light! This server might in the future be extended to include significant values of this "vperp", although under such conditions only the two relativistic kinematics retain precise self-consistency.

    Accel-One's Browser-Interactive Setup: Select 3 out of the 5 variables

    1. distance traveled dx.
    2. time elapsed e.g. dt.
    3. initial velocity e.g. v0.
    4. final velocity e.g. vf.
    5. constant acceleration a0.

    Setup Kinematic (Times & Velocities) to Use -- Only Galilean-kinematic ("Newtonian") Works Now:

    1. Galilean-kinematic velocity/chase-plane time
    2. map-time/coordinate-velocity
    3. proper-time/proper-velocity


    Other physics education links that may be of interest include those at:
    Yahoo, Quantum, c3p, McGill, ....
    Acknowledgements: Thanks to Xuewei Hu for finding and charting for us a path through the maze of unix-based query server programming, and to the UM-StL Physics & Astronomy Department for their support and encouragement.

    Send ideas/ comments/ questions/ complaints, and register for updates to this page with an email subject-field containing "accel1", to, after removing SPAMBLOCK from this e-mail address.