{"query": "Differentiate twice: position → velocity → acceleration", "count": 20, "results": [{"id": "card_works_calculus_chain", "title": "Differentiate twice: position → velocity → acceleration", "shelf": "the-works", "surface": "secular", "snippet": "A body's position goes as t³ in this toy law. Differentiate once for velocity, again for acceleration. Each differentiation is machine-checked; the second stands on the first.  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Builds on: The Riemann-Siegel acceleration. On the one map it instruments: card_question_riemann. Found from the code's own imp", "authority_tier": "engine_derived", "source": "verifier: number_theory", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_2e_2_4_acceleration_6023b87d", "title": "2.4 Acceleration — College Physics 2e", "shelf": "physics", "surface": "secular", "snippet": "2.4\n\nAcceleration\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nDefine and distinguish between instantaneous acceleration, average acceleration, and deceleration.\n\nCalculate ", "authority_tier": "reference", "source": "OpenStax: College Physics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_2e_2_4_acceleration_6023b87d", "title": "2.4 Acceleration — College Physics for AP® Courses 2e", "shelf": "physics", "surface": "secular", "snippet": "2.4\n\nAcceleration\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nDefine and distinguish between instantaneous acceleration, average acceleration, and deceleration.\n\nCalculate ", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_1_3_6_finding_velocity_and_displacement_fr_eedbae5f", "title": "3.6 Finding Velocity and Displacement from Acceleration — University Physics Volume 1", "shelf": "physics", "surface": "secular", "snippet": "3.6\n\nFinding Velocity and Displacement from Acceleration\n\nLearning Objectives\nBy the end of this section, you will be able to:\n\nDerive the kinematic equations for constant acceleration using integral ", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 1 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_2_4_acceleration_6023b87d", "title": "2.4 Acceleration — College Physics", "shelf": "physics", "surface": "secular", "snippet": "2.4\n\nAcceleration\n\nFigure\n2.12\n\nA plane decelerates, or slows down, as it comes in for landing in St. Maarten. Its acceleration is opposite in direction to its velocity. (credit: Steve Conry, Flickr)\n", "authority_tier": "reference", "source": "OpenStax: College Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_1_key_terms_df126f91", "title": "Key Terms — University Physics Volume 1", "shelf": "physics", "surface": "secular", "snippet": "Key Terms\n\nacceleration due to gravity\nacceleration of an object as a result of gravity\n\naverage acceleration\nthe rate of change in velocity; the change in velocity over time\n\naverage speed\nthe total ", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 1 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_1_3_3_average_and_instantaneous_accelerati_f6c1853f", "title": "3.3 Average and Instantaneous Acceleration — University Physics Volume 1", "shelf": "physics", "surface": "secular", "snippet": "3.3\n\nAverage and Instantaneous Acceleration\n\nLearning Objectives\nBy the end of this section, you will be able to:\n\nCalculate the average acceleration between two points in time.\n\nCalculate the instant", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 1 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_2e_glossary_8ab44681", "title": "Glossary — College Physics 2e", "shelf": "physics", "surface": "secular", "snippet": "Glossary\n\nacceleration the rate of change in velocity; the change in velocity over time\n\nacceleration due to gravity acceleration of an object as a result of gravity\n\naverage acceleration the change i", "authority_tier": "reference", "source": "OpenStax: College Physics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_glossary_32684240", "title": "Glossary — College Physics", "shelf": "physics", "surface": "secular", "snippet": "Glossary\n\nacceleration the rate of change in velocity; the change in velocity over time\n\nacceleration due to gravity acceleration of an object as a result of gravity\n\naverage acceleration the change i", "authority_tier": "reference", "source": "OpenStax: College Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_2e_glossary_786e4a8c", "title": "Glossary — College Physics for AP® Courses 2e", "shelf": "physics", "surface": "secular", "snippet": "Glossary\n\nacceleration the rate of change in velocity; the change in velocity over time\n\nacceleration due to gravity acceleration of an object as a result of gravity\n\naverage acceleration the change i", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_glossary_932099d7", "title": "Glossary — College Physics for AP® Courses", "shelf": "physics", "surface": "secular", "snippet": "Glossary\n\nacceleration the rate of change in velocity; the change in velocity over time\n\nacceleration due to gravity acceleration of an object as a result of gravity\n\naverage acceleration the change i", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_1_key_terms_a5c6aa15", "title": "Key Terms — University Physics Volume 1", "shelf": "physics", "surface": "secular", "snippet": "Key Terms\n\nacceleration vector\ninstantaneous acceleration found by taking the derivative of the velocity function with respect to time in unit vector notation\n\nangular frequency\nrate of change of an a", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 1 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_physics_concept_items_0d86aece", "title": "Concept Items — Physics", "shelf": "physics", "surface": "secular", "snippet": "Concept Items\n\n3.1\n\nAcceleration\n\n1.\n\nHow can you use the definition of acceleration to explain the units in which acceleration is measured?\n\nAcceleration is the rate of change of velocity. Therefore,", "authority_tier": "reference", "source": "OpenStax: Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_2e_2_5_motion_equations_for_constant_accele_ea2bb23c", "title": "2.5 Motion Equations for Constant Acceleration in One Dimension — College Physics 2e", "shelf": "physics", "surface": "secular", "snippet": "2.5\n\nMotion Equations for Constant Acceleration in One Dimension\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nCalculate displacement of an object that is not accelerating, g", "authority_tier": "reference", "source": "OpenStax: College Physics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_2e_2_5_motion_equations_for_constant_accele_ea2bb23c", "title": "2.5 Motion Equations for Constant Acceleration in One Dimension — College Physics for AP® Courses 2e", "shelf": "physics", "surface": "secular", "snippet": "2.5\n\nMotion Equations for Constant Acceleration in One Dimension\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nCalculate displacement of an object that is not accelerating, g", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_1_key_terms_6a9d6b89", "title": "Key Terms — University Physics Volume 1", "shelf": "physics", "surface": "secular", "snippet": "Key Terms\n\nangular acceleration\ntime rate of change of angular velocity\n\nangular position\nangle a body has rotated through in a fixed coordinate system\n\nangular velocity\ntime rate of change of angular", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 1 (CC-BY 4.0)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_works_calculus_chain"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}