DuckieDai Smart Kinematics Python Program

physics · MIT License

Overview

Solve a selected constant-acceleration quantity from the available initial velocity, final velocity, acceleration, time, and displacement values.

Tested on a TI calculator
Downloaded 41 times
Version 1.0.0
11874 bytes
Uses math

Download KINETICS.py Read the source How to install

Before you run it

TI-84 Plus CE Python · tested on OS 5.8.3, Python App 5.8.3.0048
TI Connect CE .py conversion to a Python AppVar in RAM; physically verified one program at a time
Acceleration is constant over the interval and all signed quantities share one direction convention.
A solvable combination of known values is required and divisor values cannot be zero.
Insufficient or incompatible known values produce no solution.

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Learn the math

How the kinematics equations work

The idea

Constant-acceleration motion is described by five quantities: initial velocity, final velocity, acceleration, time, and displacement. Each kinematics equation links four of them.

So if you know three, you can find a fourth. The hard part on paper is choosing the right equation; this program chooses it for you.

The formula

v = v0 + a*t

dx = v0*t + 0.5*a*t^2

v^2 = v0^2 + 2*a*dx

dx = 0.5*(v0 + v)*t

v0: initial velocity (m/s)
v: final velocity (m/s)
a: acceleration (m/s^2)
t: time (s)
dx: displacement (m)

Using the program

Choose the quantity you need: 1 final velocity, 2 initial velocity, 3 acceleration, 4 time, or 5 displacement.
Type the values the problem gives you and press Enter on any you do not know.
The program names the equation it used before showing the answer.

Worked example

A car starts from rest and accelerates at 2 m/s^2 for 5 s. How far does it go? Choose 5, enter v0 = 0, leave v blank, enter a = 2 and t = 5.

dx = v0*t + .5*a*t^2 = 0 + 0.5 x 2 x 25

The program shows dx = 25.0 meters.

Tips and common mistakes

You need three known values. With fewer the program reports that there is not enough information.
Starting from rest or coming to a stop gives you a velocity of 0 for free.
Up and down, or forward and back, need opposite signs.

Where this comes up

Constant-acceleration motion is the first major unit in almost every physics course, and the same equations return in projectile motion, free fall, and stopping-distance problems.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Smart Kinematics for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def optional_number(prompt):
    """Return a number or None if left blank."""
    while True:
        raw = input(prompt)

        if raw == "":
            return None

        try:
            value = float(raw)

            if value > -1e100 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Number or blank only.")


def show_answer(name, value, unit):
    input("Press enter for answer ")
    print("\n" * 6)
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def main():
    duckiedai_intro("KINEMATIC SOLVER")

    print("SMART KINEMATICS")
    print()
    print("What do you need?")
    print()
    print("1. Final velocity")
    print("2. Initial velocity")
    print("3. Acceleration")
    print("4. Time")
    print("5. Displacement")
    print()

    target = input("Choose 1-5: ")

    print()
    print("Enter known values.")
    print("Leave unknowns blank.")
    print()

    # -------------------------
    # GET KNOWN VALUES
    # -------------------------

    if target != "2":
        v0 = optional_number(
            "v0 (m/s): "
        )
    else:
        v0 = None

    if target != "1":
        v = optional_number(
            "v (m/s): "
        )
    else:
        v = None

    if target != "3":
        a = optional_number(
            "a (m/s^2): "
        )
    else:
        a = None

    if target != "4":
        t = optional_number(
            "t (s): "
        )
    else:
        t = None

    if target != "5":
        dx = optional_number(
            "dx (m): "
        )
    else:
        dx = None

    solved = False

    # ==================================================
    # 1. SOLVE FINAL VELOCITY
    # ==================================================

    if target == "1":

        # v = v0 + a*t

        if (v0 is not None and
                a is not None and
                t is not None):

            print()
            print("Using:")
            print("v = v0 + a*t")

            v = v0 + a * t

            print()
            print("v = " + str(v0) +
                  " + (" + str(a) +
                  " x " + str(t) + ")")

            show_answer(
                "v",
                v,
                "m/s"
            )

            solved = True

        # v^2 = v0^2 + 2*a*dx

        elif (v0 is not None and
              a is not None and
              dx is not None):

            inside = (
                v0 ** 2 +
                2 * a * dx
            )

            if inside >= 0:

                v = sqrt(inside)

                print()
                print("Using:")
                print("v^2=v0^2+2*a*dx")
                print()
                print("Rearranged:")
                print("v=+/-sqrt(")
                print("v0^2+2*a*dx)")

                print()
                print("ANSWER")
                print("v = +/- " + str(v))
                print("m/s")
                print()
                print("Direction decides")
                print("the correct sign.")

                solved = True


    # ==================================================
    # 2. SOLVE INITIAL VELOCITY
    # ==================================================

    elif target == "2":

        # v = v0 + a*t

        if (v is not None and
                a is not None and
                t is not None):

            print()
            print("Using:")
            print("v = v0 + a*t")
            print()
            print("Rearranged:")
            print("v0 = v - a*t")

            v0 = v - a * t

            show_answer(
                "v0",
                v0,
                "m/s"
            )

            solved = True

        # dx = v0*t + 0.5*a*t^2

        elif (dx is not None and
              a is not None and
              t is not None and
              t != 0):

            print()
            print("Using:")
            print("dx=v0*t+.5*a*t^2")
            print()
            print("Rearranged:")
            print("v0=(dx-.5*a*t^2)/t")

            v0 = (
                dx -
                0.5 * a * t ** 2
            ) / t

            show_answer(
                "v0",
                v0,
                "m/s"
            )

            solved = True

        # v^2 = v0^2 + 2*a*dx

        elif (v is not None and
              a is not None and
              dx is not None):

            inside = (
                v ** 2 -
                2 * a * dx
            )

            if inside >= 0:

                v0 = sqrt(inside)

                print()
                print("Using:")
                print("v^2=v0^2+2*a*dx")
                print()
                print("Rearranged:")
                print("v0=+/-sqrt(")
                print("v^2-2*a*dx)")

                print()
                print("ANSWER")
                print("v0 = +/- " + str(v0))
                print("m/s")
                print()
                print("Direction decides")
                print("the correct sign.")

                solved = True


    # ==================================================
    # 3. SOLVE ACCELERATION
    # ==================================================

    elif target == "3":

        # v = v0 + a*t

        if (v is not None and
                v0 is not None and
                t is not None and
                t != 0):

            print()
            print("Using:")
            print("v = v0 + a*t")
            print()
            print("Rearranged:")
            print("a = (v-v0)/t")

            a = (v - v0) / t

            show_answer(
                "a",
                a,
                "m/s^2"
            )

            solved = True

        # dx = v0*t + 0.5*a*t^2

        elif (dx is not None and
              v0 is not None and
              t is not None and
              t != 0):

            print()
            print("Using:")
            print("dx=v0*t+.5*a*t^2")
            print()
            print("Rearranged:")
            print("a=2(dx-v0*t)/t^2")

            a = (
                2 *
                (dx - v0 * t)
                / (t ** 2)
            )

            show_answer(
                "a",
                a,
                "m/s^2"
            )

            solved = True

        # v^2 = v0^2 + 2*a*dx

        elif (v is not None and
              v0 is not None and
              dx is not None and
              dx != 0):

            print()
            print("Using:")
            print("v^2=v0^2+2*a*dx")
            print()
            print("Rearranged:")
            print("a=(v^2-v0^2)/(2*dx)")

            a = (
                v ** 2 -
                v0 ** 2
            ) / (2 * dx)

            show_answer(
                "a",
                a,
                "m/s^2"
            )

            solved = True


    # ==================================================
    # 4. SOLVE TIME
    # ==================================================

    elif target == "4":

        # v = v0 + a*t

        if (v is not None and
                v0 is not None and
                a is not None and
                a != 0):

            print()
            print("Using:")
            print("v = v0 + a*t")
            print()
            print("Rearranged:")
            print("t = (v-v0)/a")

            t = (v - v0) / a

            show_answer(
                "t",
                t,
                "seconds"
            )

            solved = True

        # dx = v0*t + 0.5*a*t^2

        elif (dx is not None and
              v0 is not None and
              a is not None):

            print()
            print("Using:")
            print("dx=v0*t+.5*a*t^2")

            if a == 0:

                if v0 != 0:

                    t = dx / v0

                    print()
                    print("Since a = 0:")
                    print("t = dx/v0")

                    show_answer(
                        "t",
                        t,
                        "seconds"
                    )

                    solved = True

            else:

                inside = (
                    v0 ** 2 +
                    2 * a * dx
                )

                if inside >= 0:

                    root = sqrt(inside)

                    t1 = (
                        -v0 + root
                    ) / a

                    t2 = (
                        -v0 - root
                    ) / a

                    print()
                    print("Solving quadratic:")
                    print()

                    if t1 >= 0:
                        print("t = " + str(t1) +
                              " s")

                    if t2 >= 0:
                        print("t = " + str(t2) +
                              " s")

                    print()
                    print("Use physical")
                    print("positive time.")

                    solved = True


    # ==================================================
    # 5. SOLVE DISPLACEMENT
    # ==================================================

    elif target == "5":

        # dx = v0*t + 0.5*a*t^2

        if (v0 is not None and
                a is not None and
                t is not None):

            print()
            print("Using:")
            print("dx=v0*t+.5*a*t^2")

            dx = (
                v0 * t +
                0.5 * a * t ** 2
            )

            show_answer(
                "dx",
                dx,
                "meters"
            )

            solved = True

        # v^2 = v0^2 + 2*a*dx

        elif (v is not None and
              v0 is not None and
              a is not None and
              a != 0):

            print()
            print("Using:")
            print("v^2=v0^2+2*a*dx")
            print()
            print("Rearranged:")
            print("dx=(v^2-v0^2)/(2*a)")

            dx = (
                v ** 2 -
                v0 ** 2
            ) / (2 * a)

            show_answer(
                "dx",
                dx,
                "meters"
            )

            solved = True


    # ==================================================
    # COULD NOT SOLVE
    # ==================================================

    if not solved:
        print()
        print("Not enough usable")
        print("information.")
        print()
        print("Check the values")
        print("given in the problem.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Smart Kinematics for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def optional_number(prompt):
"""Return a number or None if left blank."""
while True:
raw = input(prompt)
if raw == "":
return None
try:
value = float(raw)
if value > -1e100 and value < 1e100:
return value
except ValueError:
pass
print("Number or blank only.")
def show_answer(name, value, unit):
input("Press enter for answer ")
print("\n" * 6)
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def main():
duckiedai_intro("KINEMATIC SOLVER")
print("SMART KINEMATICS")
print()
print("What do you need?")
print()
print("1. Final velocity")
print("2. Initial velocity")
print("3. Acceleration")
print("4. Time")
print("5. Displacement")
print()
target = input("Choose 1-5: ")
print()
print("Enter known values.")
print("Leave unknowns blank.")
print()
# -------------------------
# GET KNOWN VALUES
# -------------------------
if target != "2":
v0 = optional_number(
"v0 (m/s): "
)
else:
v0 = None
if target != "1":
v = optional_number(
"v (m/s): "
)
else:
v = None
if target != "3":
a = optional_number(
"a (m/s^2): "
)
else:
a = None
if target != "4":
t = optional_number(
"t (s): "
)
else:
t = None
if target != "5":
dx = optional_number(
"dx (m): "
)
else:
dx = None
solved = False
# ==================================================
# 1. SOLVE FINAL VELOCITY
# ==================================================
if target == "1":
# v = v0 + a*t
if (v0 is not None and
a is not None and
t is not None):
print()
print("Using:")
print("v = v0 + a*t")
v = v0 + a * t
print()
print("v = " + str(v0) +
" + (" + str(a) +
" x " + str(t) + ")")
show_answer(
"v",
v,
"m/s"
)
solved = True
# v^2 = v0^2 + 2*a*dx
elif (v0 is not None and
a is not None and
dx is not None):
inside = (
v0 ** 2 +
2 * a * dx
)
if inside >= 0:
v = sqrt(inside)
print()
print("Using:")
print("v^2=v0^2+2*a*dx")
print()
print("Rearranged:")
print("v=+/-sqrt(")
print("v0^2+2*a*dx)")
print()
print("ANSWER")
print("v = +/- " + str(v))
print("m/s")
print()
print("Direction decides")
print("the correct sign.")
solved = True
# ==================================================
# 2. SOLVE INITIAL VELOCITY
# ==================================================
elif target == "2":
# v = v0 + a*t
if (v is not None and
a is not None and
t is not None):
print()
print("Using:")
print("v = v0 + a*t")
print()
print("Rearranged:")
print("v0 = v - a*t")
v0 = v - a * t
show_answer(
"v0",
v0,
"m/s"
)
solved = True
# dx = v0*t + 0.5*a*t^2
elif (dx is not None and
a is not None and
t is not None and
t != 0):
print()
print("Using:")
print("dx=v0*t+.5*a*t^2")
print()
print("Rearranged:")
print("v0=(dx-.5*a*t^2)/t")
v0 = (
dx -
0.5 * a * t ** 2
) / t
show_answer(
"v0",
v0,
"m/s"
)
solved = True
# v^2 = v0^2 + 2*a*dx
elif (v is not None and
a is not None and
dx is not None):
inside = (
v ** 2 -
2 * a * dx
)
if inside >= 0:
v0 = sqrt(inside)
print()
print("Using:")
print("v^2=v0^2+2*a*dx")
print()
print("Rearranged:")
print("v0=+/-sqrt(")
print("v^2-2*a*dx)")
print()
print("ANSWER")
print("v0 = +/- " + str(v0))
print("m/s")
print()
print("Direction decides")
print("the correct sign.")
solved = True
# ==================================================
# 3. SOLVE ACCELERATION
# ==================================================
elif target == "3":
# v = v0 + a*t
if (v is not None and
v0 is not None and
t is not None and
t != 0):
print()
print("Using:")
print("v = v0 + a*t")
print()
print("Rearranged:")
print("a = (v-v0)/t")
a = (v - v0) / t
show_answer(
"a",
a,
"m/s^2"
)
solved = True
# dx = v0*t + 0.5*a*t^2
elif (dx is not None and
v0 is not None and
t is not None and
t != 0):
print()
print("Using:")
print("dx=v0*t+.5*a*t^2")
print()
print("Rearranged:")
print("a=2(dx-v0*t)/t^2")
a = (
2 *
(dx - v0 * t)
/ (t ** 2)
)
show_answer(
"a",
a,
"m/s^2"
)
solved = True
# v^2 = v0^2 + 2*a*dx
elif (v is not None and
v0 is not None and
dx is not None and
dx != 0):
print()
print("Using:")
print("v^2=v0^2+2*a*dx")
print()
print("Rearranged:")
print("a=(v^2-v0^2)/(2*dx)")
a = (
v ** 2 -
v0 ** 2
) / (2 * dx)
show_answer(
"a",
a,
"m/s^2"
)
solved = True
# ==================================================
# 4. SOLVE TIME
# ==================================================
elif target == "4":
# v = v0 + a*t
if (v is not None and
v0 is not None and
a is not None and
a != 0):
print()
print("Using:")
print("v = v0 + a*t")
print()
print("Rearranged:")
print("t = (v-v0)/a")
t = (v - v0) / a
show_answer(
"t",
t,
"seconds"
)
solved = True
# dx = v0*t + 0.5*a*t^2
elif (dx is not None and
v0 is not None and
a is not None):
print()
print("Using:")
print("dx=v0*t+.5*a*t^2")
if a == 0:
if v0 != 0:
t = dx / v0
print()
print("Since a = 0:")
print("t = dx/v0")
show_answer(
"t",
t,
"seconds"
)
solved = True
else:
inside = (
v0 ** 2 +
2 * a * dx
)
if inside >= 0:
root = sqrt(inside)
t1 = (
-v0 + root
) / a
t2 = (
-v0 - root
) / a
print()
print("Solving quadratic:")
print()
if t1 >= 0:
print("t = " + str(t1) +
" s")
if t2 >= 0:
print("t = " + str(t2) +
" s")
print()
print("Use physical")
print("positive time.")
solved = True
# ==================================================
# 5. SOLVE DISPLACEMENT
# ==================================================
elif target == "5":
# dx = v0*t + 0.5*a*t^2
if (v0 is not None and
a is not None and
t is not None):
print()
print("Using:")
print("dx=v0*t+.5*a*t^2")
dx = (
v0 * t +
0.5 * a * t ** 2
)
show_answer(
"dx",
dx,
"meters"
)
solved = True
# v^2 = v0^2 + 2*a*dx
elif (v is not None and
v0 is not None and
a is not None and
a != 0):
print()
print("Using:")
print("v^2=v0^2+2*a*dx")
print()
print("Rearranged:")
print("dx=(v^2-v0^2)/(2*a)")
dx = (
v ** 2 -
v0 ** 2
) / (2 * a)
show_answer(
"dx",
dx,
"meters"
)
solved = True
# ==================================================
# COULD NOT SOLVE
# ==================================================
if not solved:
print()
print("Not enough usable")
print("information.")
print()
print("Check the values")
print("given in the problem.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: KINETICS.py
Size: 11874 bytes
SHA-256: 5eb4efc0bee4bd73379ac513a08f05d889af8185695ff95053f6bbca30ec6bc2

Usage

Inputs

Target quantity
Known velocity, acceleration, time, and displacement values; unknown values are left blank

Outputs

Solved target with the selected constant-acceleration equation and labelled unit

Units: Use one consistent system such as metres, seconds, metres per second, and metres per second squared.

Assumptions and limitations

Assumptions

Acceleration is constant over the interval and all signed quantities share one direction convention.

Constraints

A solvable combination of known values is required and divisor values cannot be zero.

Known failures

Insufficient or incompatible known values produce no solution.
Some quadratic situations may have multiple physical interpretations requiring user judgment.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact paginated .py transferred through TI Connect CE into RAM and tested individually
What happened: Passed: branded intro, target selection, optional value entry, compatible kinematics solution, and paginated answer screen ran on the physical calculator
Dependencies: math
Suggested calculator name: KINETICS — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as KINETICS or another name, then open the Python App and try the worked example on this page first.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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