Random Uniform Motion Exercise Generator
Build a bounded reproducible uniform motion exercise from explicitly supplied candidate scenarios. Every candidate must satisfy imported physics/average-speed before selection; answer cards preserve its units, conventions, domain limitations and signed/unknown results. Draws are uniform over caller candidate positions; no replacement means no repeated positions, not necessarily distinct answers. No automatic pedagogical correctness, compliance or physical readiness.
Description
Average speed relates traveled distance to elapsed time under the imported calculator’s units.
Average speed relates traveled distance to elapsed time under the imported calculator’s units.1
Sampled scenarios provide arithmetic practice without inferring an acceleration history.
When to use Random Uniform Motion Exercise Generator
Use this tool when you need to assemble reproducible practice cards from a supplied, validated scenario corpus. Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
How to use Random Uniform Motion Exercise Generator and understand its results
- Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
- Enter seed, count, withoutReplacement, candidateInputsJson, following the field table and calculation rules below, then run the tool.
- Read result. Inspect the nested fields in the output table below and keep any missing evidence or selected indices visible.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| seed | Nonblank reproducibility seed; default seeded runs restart for each request | string | Required |
| count | Number of sampled entry positions | safe integer from 1 to 64 | Required |
| withoutReplacement | True draws distinct entry positions; false permits repeated positions | boolean | Required |
| candidateInputsJson | JSON strings containing full candidate input objects for the imported calculator | list of string | Required |
Enter 1–128 dense candidateInputsJson strings, each a strict JSON object for the imported calculator. Each string is at most 8192 UTF-16 units, the corpus at most 131072, and nesting at most 16 levels; nonfinite numbers and prototype-control keys are rejected. Select candidate positions under the sampling rules, then validate every candidate, including undrawn ones, by invoking the imported calculator with a fixed random source of 0.5. Any invalid candidate fails the whole request. Invoke it again for selected candidates with the request’s advancing source, and return original inputs, actual answer objects, selected indices, and never-selected indices. Duplicate candidate texts or equal answers may occur at distinct positions.2, 3, 4
Use a nonblank seed of at most 256 UTF-16 units and a safe-integer count from 1 to 64. By default the seed is hashed into a deterministic pseudorandom state; each run restarts that state, so identical full inputs and implementation reproduce the result. The SDK may provide context.random, which replaces the seeded source and advances across the request; the seed remains required. Every source value must be finite in [0,1), with a request limit of 100000 source calls. Draw an index as floor(U×remainingSize). With replacement draw from the full inventory each time; without replacement remove each chosen position from an ordered pool and reject counts exceeding the inventory size. Uniform-source draws are over positions, not necessarily distinct values. This is not secure randomness.
The imported average-speed calculator divides supplied distance by strictly positive time. Units follow the candidate fields; the implementation does not infer motion history or enforce nonnegative distance.
speed=distance/time Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the fields below | object |
| result.baseToolId | Canonical ID of the imported calculator that produces answer cards | string |
| result.selectedCandidateIndices | Zero-based original corpus positions, in draw order | list |
| result.unusedCandidateIndices | Zero-based original corpus positions never selected | list |
| result.exercises | Selected cards with original input and actual imported answer objects | list |
Each result.exercises entry preserves its supplied input and imported answer object. Additional roundTripAnswer, secondaryAnswer, prompts, or derived quantities appear only where the mechanics above describe them. selectedCandidateIndices and unusedCandidateIndices refer to the original corpus positions, not answer values.
{
"input": {
"seed": "tool.io/batch42",
"count": 1,
"withoutReplacement": true,
"candidateInputsJson": [
"{\"distance\": 100, \"time\": 5}"
]
},
"output": {
"result": {
"baseToolId": "physics/average-speed",
"selectedCandidateIndices": [
0
],
"unusedCandidateIndices": [],
"exercises": [
{
"input": {
"distance": 100,
"time": 5
},
"answer": {
"speed": 20
}
}
]
}
}
}Limitations and assumptions
The default source is deterministic pseudorandomness, not an independently audited or secure draw. Replacement applies to inventory positions; distinct positions may render identically or yield equal answers. Review the supplied inventory or scenario domain independently before interpreting the sample. Each answer retains the imported calculator’s unit conventions and domain assumptions. Randomizing a supplied scenario does not broaden that calculator’s capabilities.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related task, use Random Projectile Motion Scenario Generator: An ideal projectile model assumes a stated gravity and launch convention. Supplied scenarios preserve those assumptions rather than providing real-world trajectory or safety predictions. For a complementary step, use Random Momentum and Impulse Exercise Generator: Impulse changes signed momentum under a one-dimensional constant-mass model. Combining sampled constant-force scenarios with an explicit initial velocity keeps initial and final states comparable.
References
Similar or alternative tools
- Random Projectile Motion Scenario Generator
An ideal projectile model assumes a stated gravity and launch convention. Supplied scenarios preserve those assumptions rather than providing real-world trajectory or safety predictions.
- Random Momentum and Impulse Exercise Generator
Impulse changes signed momentum under a one-dimensional constant-mass model. Combining sampled constant-force scenarios with an explicit initial velocity keeps initial and final states comparable.