task_physics__motion_graph__interval_displacement_value

Summary

• Domain: physics
• Scene id: motion_graph
• Implementation scene: motion_graph
• Implementation source: src/trace_tasks/tasks/physics/motion_graph/interval_displacement_value.py

Task Contract

Computes the integer displacement over a marked interval on a velocity-time graph.

Program Contract

Program: integer(area_under_velocity_time_curve(marked_interval, segment_mode=constant_velocity_or_constant_acceleration)); scene=motion_graph; scope=interval_displacement_value

Candidate set: the visible graph curve, marked interval, axis scales, labels, and option cells when present inside the interval_displacement_value objective scope. Operands: marked_interval (semantic_role, allowed highlighted_time_interval_on_velocity_time_graph, source program_schema_concrete); velocity_segment (semantic_role, allowed constant_or_linearly_changing_velocity_segment, source program_schema_concrete); axis_scale (semantic_role, allowed visible_integer_time_and_velocity_axis_scale, source program_schema_concrete); active query_id branch when present. Operation: evaluate integer over the candidate set using the visible quantities, relations, branch semantics, and formulas encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the integer schema; The answer value is the displacement in meters over the marked interval. Annotation witnesses: segment witnesses from the finalized render. Annotation value: [[x0, y0], [x1, y1]] for the marked velocity-time graph segment, where each endpoint is a [x, y] pixel point. Annotation must mark the minimal visual segment witness for the marked interval. It must not mark derived displacement text, prompt-only formulas, decorative panel chrome, broad axis-scale regions, or unrelated graph segments. Query ids: constant_velocity_interval_displacement, constant_acceleration_interval_displacement.

Reasoning Operations

Families: formula_evaluation

Query Branches

Query id	Program schema
constant_velocity_interval_displacement	integer(area_under_velocity_time_curve(marked_interval, segment_mode=constant_velocity)); scene=motion_graph; scope=interval_displacement_value
constant_acceleration_interval_displacement	integer(area_under_velocity_time_curve(marked_interval, segment_mode=constant_acceleration)); scene=motion_graph; scope=interval_displacement_value

Program Metadata

• Program signatures: physics.motion_graph_interval_displacement
• Base program contract: integer(area_under_velocity_time_curve(marked_interval, segment_mode=constant_velocity_or_constant_acceleration)); scene=motion_graph; scope=interval_displacement_value
• Parameter axes: query_id, scene_variant, interval_width, velocity_endpoints
• Arguments:
• marked_interval: semantic_role; allowed highlighted_time_interval_on_velocity_time_graph; source program_schema_concrete
• velocity_segment: semantic_role; allowed constant_or_linearly_changing_velocity_segment; source program_schema_concrete
• axis_scale: semantic_role; allowed visible_integer_time_and_velocity_axis_scale; source program_schema_concrete
• Argument metadata status: curated
• Supported query_ids: constant_velocity_interval_displacement, constant_acceleration_interval_displacement

Answer Contract

• Answer schema: integer
• Generator answer_gt.type: integer
• The answer value is the displacement in meters over the marked interval.

Annotation Contract

• Annotation schema: segment
• Generator annotation_gt.type: segment
• Annotation value: [[x0, y0], [x1, y1]] for the marked velocity-time graph segment, where each endpoint is a [x, y] pixel point.
• Annotation must mark the minimal visual segment witness for the marked interval. It must not mark derived displacement text, prompt-only formulas, decorative panel chrome, broad axis-scale regions, or unrelated graph segments.
• Annotation and answer must be projected from the same generated execution trace, not inferred from pixels or prompt text.

Prompt And Trace Requirements

• Prompt text must come from the physics motion-graph v1 prompt bundle, with scene and task/query layers selected deterministically and recorded in metadata.
• Constant-velocity intervals use rectangle area v * delta_t; constant-acceleration intervals use trapezoid area ((v_start + v_end) / 2) * delta_t.
• Endpoint values and interval widths must be sampled so the answer is integer-valued.
• Render randomness, sampled fonts/styles, marked interval, curve values, and verifier payloads must be explicit in the instance trace.