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DuckieDai Smart Kinematics

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

Version 1.0.0 · Tested on a TI calculator

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physics · MIT License

Overview

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

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.

Browser preview

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Exact reviewed bytes

Source code

Download .py

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  1. """DuckieDai Smart Kinematics for TI-84 Plus CE Python."""
  3. from math import sqrt
  6. def duckiedai_intro(program_name, wait=True):
  7. """Show the reusable DuckieDai program opening."""
  8. title = program_name[:16]
  9. empty = 16 - len(title)
  10. left = empty // 2
  11. right = empty - left
  13. print("+----------------------+")
  14. print("| " + " " * left + title + " " * right + " |")
  15. print("| |")
  16. print("| __ |")
  17. print("| ___(o )> quack! |")
  18. print("| \\ <_. ) |")
  19. print("| `---' |")
  20. print("| by DuckieDai |")
  21. print("+----------------------+")
  22. print("Loading...")
  24. if wait:
  25. input("Press enter to start ")
  26. print("\n" * 6)
  29. def optional_number(prompt):
  30. """Return a number or None if left blank."""
  31. while True:
  32. raw = input(prompt)
  34. if raw == "":
  35. return None
  37. try:
  38. value = float(raw)
  40. if value > -1e100 and value < 1e100:
  41. return value
  43. except ValueError:
  44. pass
  46. print("Number or blank only.")
  49. def show_answer(name, value, unit):
  50. input("Press enter for answer ")
  51. print("\n" * 6)
  52. print("ANSWER")
  53. print(name + " = " + str(value))
  54. print(unit)
  57. def main():
  58. duckiedai_intro("KINEMATIC SOLVER")
  60. print("SMART KINEMATICS")
  61. print()
  62. print("What do you need?")
  63. print()
  64. print("1. Final velocity")
  65. print("2. Initial velocity")
  66. print("3. Acceleration")
  67. print("4. Time")
  68. print("5. Displacement")
  69. print()
  71. target = input("Choose 1-5: ")
  73. print()
  74. print("Enter known values.")
  75. print("Leave unknowns blank.")
  76. print()
  78. # -------------------------
  79. # GET KNOWN VALUES
  80. # -------------------------
  82. if target != "2":
  83. v0 = optional_number(
  84. "v0 (m/s): "
  85. )
  86. else:
  87. v0 = None
  89. if target != "1":
  90. v = optional_number(
  91. "v (m/s): "
  92. )
  93. else:
  94. v = None
  96. if target != "3":
  97. a = optional_number(
  98. "a (m/s^2): "
  99. )
  100. else:
  101. a = None
  103. if target != "4":
  104. t = optional_number(
  105. "t (s): "
  106. )
  107. else:
  108. t = None
  110. if target != "5":
  111. dx = optional_number(
  112. "dx (m): "
  113. )
  114. else:
  115. dx = None
  117. solved = False
  119. # ==================================================
  120. # 1. SOLVE FINAL VELOCITY
  121. # ==================================================
  123. if target == "1":
  125. # v = v0 + a*t
  127. if (v0 is not None and
  128. a is not None and
  129. t is not None):
  131. print()
  132. print("Using:")
  133. print("v = v0 + a*t")
  135. v = v0 + a * t
  137. print()
  138. print("v = " + str(v0) +
  139. " + (" + str(a) +
  140. " x " + str(t) + ")")
  142. show_answer(
  143. "v",
  144. v,
  145. "m/s"
  146. )
  148. solved = True
  150. # v^2 = v0^2 + 2*a*dx
  152. elif (v0 is not None and
  153. a is not None and
  154. dx is not None):
  156. inside = (
  157. v0 ** 2 +
  158. 2 * a * dx
  159. )
  161. if inside >= 0:
  163. v = sqrt(inside)
  165. print()
  166. print("Using:")
  167. print("v^2=v0^2+2*a*dx")
  168. print()
  169. print("Rearranged:")
  170. print("v=+/-sqrt(")
  171. print("v0^2+2*a*dx)")
  173. print()
  174. print("ANSWER")
  175. print("v = +/- " + str(v))
  176. print("m/s")
  177. print()
  178. print("Direction decides")
  179. print("the correct sign.")
  181. solved = True
  184. # ==================================================
  185. # 2. SOLVE INITIAL VELOCITY
  186. # ==================================================
  188. elif target == "2":
  190. # v = v0 + a*t
  192. if (v is not None and
  193. a is not None and
  194. t is not None):
  196. print()
  197. print("Using:")
  198. print("v = v0 + a*t")
  199. print()
  200. print("Rearranged:")
  201. print("v0 = v - a*t")
  203. v0 = v - a * t
  205. show_answer(
  206. "v0",
  207. v0,
  208. "m/s"
  209. )
  211. solved = True
  213. # dx = v0*t + 0.5*a*t^2
  215. elif (dx is not None and
  216. a is not None and
  217. t is not None and
  218. t != 0):
  220. print()
  221. print("Using:")
  222. print("dx=v0*t+.5*a*t^2")
  223. print()
  224. print("Rearranged:")
  225. print("v0=(dx-.5*a*t^2)/t")
  227. v0 = (
  228. dx -
  229. 0.5 * a * t ** 2
  230. ) / t
  232. show_answer(
  233. "v0",
  234. v0,
  235. "m/s"
  236. )
  238. solved = True
  240. # v^2 = v0^2 + 2*a*dx
  242. elif (v is not None and
  243. a is not None and
  244. dx is not None):
  246. inside = (
  247. v ** 2 -
  248. 2 * a * dx
  249. )
  251. if inside >= 0:
  253. v0 = sqrt(inside)
  255. print()
  256. print("Using:")
  257. print("v^2=v0^2+2*a*dx")
  258. print()
  259. print("Rearranged:")
  260. print("v0=+/-sqrt(")
  261. print("v^2-2*a*dx)")
  263. print()
  264. print("ANSWER")
  265. print("v0 = +/- " + str(v0))
  266. print("m/s")
  267. print()
  268. print("Direction decides")
  269. print("the correct sign.")
  271. solved = True
  274. # ==================================================
  275. # 3. SOLVE ACCELERATION
  276. # ==================================================
  278. elif target == "3":
  280. # v = v0 + a*t
  282. if (v is not None and
  283. v0 is not None and
  284. t is not None and
  285. t != 0):
  287. print()
  288. print("Using:")
  289. print("v = v0 + a*t")
  290. print()
  291. print("Rearranged:")
  292. print("a = (v-v0)/t")
  294. a = (v - v0) / t
  296. show_answer(
  297. "a",
  298. a,
  299. "m/s^2"
  300. )
  302. solved = True
  304. # dx = v0*t + 0.5*a*t^2
  306. elif (dx is not None and
  307. v0 is not None and
  308. t is not None and
  309. t != 0):
  311. print()
  312. print("Using:")
  313. print("dx=v0*t+.5*a*t^2")
  314. print()
  315. print("Rearranged:")
  316. print("a=2(dx-v0*t)/t^2")
  318. a = (
  319. 2 *
  320. (dx - v0 * t)
  321. / (t ** 2)
  322. )
  324. show_answer(
  325. "a",
  326. a,
  327. "m/s^2"
  328. )
  330. solved = True
  332. # v^2 = v0^2 + 2*a*dx
  334. elif (v is not None and
  335. v0 is not None and
  336. dx is not None and
  337. dx != 0):
  339. print()
  340. print("Using:")
  341. print("v^2=v0^2+2*a*dx")
  342. print()
  343. print("Rearranged:")
  344. print("a=(v^2-v0^2)/(2*dx)")
  346. a = (
  347. v ** 2 -
  348. v0 ** 2
  349. ) / (2 * dx)
  351. show_answer(
  352. "a",
  353. a,
  354. "m/s^2"
  355. )
  357. solved = True
  360. # ==================================================
  361. # 4. SOLVE TIME
  362. # ==================================================
  364. elif target == "4":
  366. # v = v0 + a*t
  368. if (v is not None and
  369. v0 is not None and
  370. a is not None and
  371. a != 0):
  373. print()
  374. print("Using:")
  375. print("v = v0 + a*t")
  376. print()
  377. print("Rearranged:")
  378. print("t = (v-v0)/a")
  380. t = (v - v0) / a
  382. show_answer(
  383. "t",
  384. t,
  385. "seconds"
  386. )
  388. solved = True
  390. # dx = v0*t + 0.5*a*t^2
  392. elif (dx is not None and
  393. v0 is not None and
  394. a is not None):
  396. print()
  397. print("Using:")
  398. print("dx=v0*t+.5*a*t^2")
  400. if a == 0:
  402. if v0 != 0:
  404. t = dx / v0
  406. print()
  407. print("Since a = 0:")
  408. print("t = dx/v0")
  410. show_answer(
  411. "t",
  412. t,
  413. "seconds"
  414. )
  416. solved = True
  418. else:
  420. inside = (
  421. v0 ** 2 +
  422. 2 * a * dx
  423. )
  425. if inside >= 0:
  427. root = sqrt(inside)
  429. t1 = (
  430. -v0 + root
  431. ) / a
  433. t2 = (
  434. -v0 - root
  435. ) / a
  437. print()
  438. print("Solving quadratic:")
  439. print()
  441. if t1 >= 0:
  442. print("t = " + str(t1) +
  443. " s")
  445. if t2 >= 0:
  446. print("t = " + str(t2) +
  447. " s")
  449. print()
  450. print("Use physical")
  451. print("positive time.")
  453. solved = True
  456. # ==================================================
  457. # 5. SOLVE DISPLACEMENT
  458. # ==================================================
  460. elif target == "5":
  462. # dx = v0*t + 0.5*a*t^2
  464. if (v0 is not None and
  465. a is not None and
  466. t is not None):
  468. print()
  469. print("Using:")
  470. print("dx=v0*t+.5*a*t^2")
  472. dx = (
  473. v0 * t +
  474. 0.5 * a * t ** 2
  475. )
  477. show_answer(
  478. "dx",
  479. dx,
  480. "meters"
  481. )
  483. solved = True
  485. # v^2 = v0^2 + 2*a*dx
  487. elif (v is not None and
  488. v0 is not None and
  489. a is not None and
  490. a != 0):
  492. print()
  493. print("Using:")
  494. print("v^2=v0^2+2*a*dx")
  495. print()
  496. print("Rearranged:")
  497. print("dx=(v^2-v0^2)/(2*a)")
  499. dx = (
  500. v ** 2 -
  501. v0 ** 2
  502. ) / (2 * a)
  504. show_answer(
  505. "dx",
  506. dx,
  507. "meters"
  508. )
  510. solved = True
  513. # ==================================================
  514. # COULD NOT SOLVE
  515. # ==================================================
  517. if not solved:
  518. print()
  519. print("Not enough usable")
  520. print("information.")
  521. print()
  522. print("Check the values")
  523. print("given in the problem.")
  525. print()
  526. print("DuckieDai says: done!")
  529. # TI-Python imports the selected AppVar rather than
  530. # setting __name__ to main.
  531. main()
Filename
KINETICS.py
Size
11874 bytes
SHA-256
5eb4efc0bee4bd73379ac513a08f05d889af8185695ff95053f6bbca30ec6bc2

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  2. Download the .py source above and verify its SHA-256 digest if your computer provides that option.
  3. Use TI Connect CE to send the Python file to a compatible calculator. KINETICS is a suggested name; you may choose another valid, unique calculator name.
  4. Open the Python App, select the program, and check sample inputs before relying on other results.

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