Table of contents
- 0. Math Review(0)
- 1. Intro to Physics Units(0)
- 2. 1D Motion / Kinematics(0)
- Vectors, Scalars, & Displacement(0)
- Average Velocity(0)
- Intro to Acceleration(0)
- Position-Time Graphs & Velocity(0)
- Conceptual Problems with Position-Time Graphs(0)
- Velocity-Time Graphs & Acceleration(0)
- Calculating Displacement from Velocity-Time Graphs(0)
- Conceptual Problems with Velocity-Time Graphs(0)
- Calculating Change in Velocity from Acceleration-Time Graphs(0)
- Graphing Position, Velocity, and Acceleration Graphs(0)
- Kinematics Equations(0)
- Vertical Motion and Free Fall(0)
- Catch/Overtake Problems(0)
- 3. Vectors(0)
- Review of Vectors vs. Scalars(0)
- Introduction to Vectors(0)
- Adding Vectors Graphically(0)
- Vector Composition & Decomposition(0)
- Adding Vectors by Components(0)
- Trig Review(0)
- Unit Vectors(0)
- Introduction to Dot Product (Scalar Product)(0)
- Calculating Dot Product Using Components(0)
- Intro to Cross Product (Vector Product)(0)
- Calculating Cross Product Using Components(0)
- 4. 2D Kinematics(0)
- 5. Projectile Motion(0)
- 6. Intro to Forces (Dynamics)(0)
- 7. Friction, Inclines, Systems(0)
- 8. Centripetal Forces & Gravitation(0)
- Uniform Circular Motion(0)
- Period and Frequency in Uniform Circular Motion(0)
- Centripetal Forces(0)
- Vertical Centripetal Forces(0)
- Flat Curves(0)
- Banked Curves(0)
- Newton's Law of Gravity(0)
- Gravitational Forces in 2D(0)
- Acceleration Due to Gravity(0)
- Satellite Motion: Intro(0)
- Satellite Motion: Speed & Period(0)
- Geosynchronous Orbits(0)
- Overview of Kepler's Laws(0)
- Kepler's First Law(0)
- Kepler's Third Law(0)
- Kepler's Third Law for Elliptical Orbits(0)
- Gravitational Potential Energy(0)
- Gravitational Potential Energy for Systems of Masses(0)
- Escape Velocity(0)
- Energy of Circular Orbits(0)
- Energy of Elliptical Orbits(0)
- Black Holes(0)
- Gravitational Force Inside the Earth(0)
- Mass Distribution with Calculus(0)
- 9. Work & Energy(0)
- 10. Conservation of Energy(0)
- Intro to Energy Types(0)
- Gravitational Potential Energy(0)
- Intro to Conservation of Energy(0)
- Energy with Non-Conservative Forces(0)
- Springs & Elastic Potential Energy(0)
- Solving Projectile Motion Using Energy(0)
- Motion Along Curved Paths(0)
- Rollercoaster Problems(0)
- Pendulum Problems(0)
- Energy in Connected Objects (Systems)(0)
- Force & Potential Energy(0)
- 11. Momentum & Impulse(0)
- Intro to Momentum(0)
- Intro to Impulse(0)
- Impulse with Variable Forces(0)
- Intro to Conservation of Momentum(0)
- Push-Away Problems(0)
- Types of Collisions(0)
- Completely Inelastic Collisions(0)
- Adding Mass to a Moving System(0)
- Collisions & Motion (Momentum & Energy)(0)
- Ballistic Pendulum(0)
- Collisions with Springs(0)
- Elastic Collisions(0)
- How to Identify the Type of Collision(0)
- Intro to Center of Mass(0)
- 12. Rotational Kinematics(0)
- 13. Rotational Inertia & Energy(0)
- More Conservation of Energy Problems(0)
- Conservation of Energy in Rolling Motion(0)
- Parallel Axis Theorem(0)
- Intro to Moment of Inertia(0)
- Moment of Inertia via Integration(0)
- Moment of Inertia of Systems(0)
- Moment of Inertia & Mass Distribution(0)
- Intro to Rotational Kinetic Energy(0)
- Energy of Rolling Motion(0)
- Types of Motion & Energy(0)
- Conservation of Energy with Rotation(0)
- Torque with Kinematic Equations(0)
- Rotational Dynamics with Two Motions(0)
- Rotational Dynamics of Rolling Motion(0)
- 14. Torque & Rotational Dynamics(0)
- 15. Rotational Equilibrium(0)
- 16. Angular Momentum(0)
- Opening/Closing Arms on Rotating Stool(0)
- Conservation of Angular Momentum(0)
- Angular Momentum & Newton's Second Law(0)
- Intro to Angular Collisions(0)
- Jumping Into/Out of Moving Disc(0)
- Spinning on String of Variable Length(0)
- Angular Collisions with Linear Motion(0)
- Intro to Angular Momentum(0)
- Angular Momentum of a Point Mass(0)
- Angular Momentum of Objects in Linear Motion(0)
- 17. Periodic Motion(0)
- 18. Waves & Sound(0)
- Intro to Waves(0)
- Velocity of Transverse Waves(0)
- Velocity of Longitudinal Waves(0)
- Wave Functions(0)
- Phase Constant(0)
- Average Power of Waves on Strings(0)
- Wave Intensity(0)
- Sound Intensity(0)
- Wave Interference(0)
- Superposition of Wave Functions(0)
- Standing Waves(0)
- Standing Wave Functions(0)
- Standing Sound Waves(0)
- Beats(0)
- The Doppler Effect(0)
- 19. Fluid Mechanics(0)
- 20. Heat and Temperature(0)
- Temperature(0)
- Linear Thermal Expansion(0)
- Volume Thermal Expansion(0)
- Moles and Avogadro's Number(0)
- Specific Heat & Temperature Changes(0)
- Latent Heat & Phase Changes(0)
- Intro to Calorimetry(0)
- Calorimetry with Temperature and Phase Changes(0)
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes(0)
- Phase Diagrams, Triple Points and Critical Points(0)
- Heat Transfer(0)
- 21. Kinetic Theory of Ideal Gases(0)
- 22. The First Law of Thermodynamics(0)
- 23. The Second Law of Thermodynamics(0)
- 24. Electric Force & Field; Gauss' Law(0)
- 25. Electric Potential(0)
- 26. Capacitors & Dielectrics(0)
- 27. Resistors & DC Circuits(0)
- 28. Magnetic Fields and Forces(0)
- 29. Sources of Magnetic Field(0)
- Magnetic Field Produced by Moving Charges(0)
- Magnetic Field Produced by Straight Currents(0)
- Magnetic Force Between Parallel Currents(0)
- Magnetic Force Between Two Moving Charges(0)
- Magnetic Field Produced by Loops and Solenoids(0)
- Toroidal Solenoids aka Toroids(0)
- Biot-Savart Law (Calculus)(0)
- Ampere's Law (Calculus)(0)
- 30. Induction and Inductance(0)
- 31. Alternating Current(0)
- Alternating Voltages and Currents(0)
- RMS Current and Voltage(0)
- Phasors(0)
- Resistors in AC Circuits(0)
- Phasors for Resistors(0)
- Capacitors in AC Circuits(0)
- Phasors for Capacitors(0)
- Inductors in AC Circuits(0)
- Phasors for Inductors(0)
- Impedance in AC Circuits(0)
- Series LRC Circuits(0)
- Resonance in Series LRC Circuits(0)
- Power in AC Circuits(0)
- 32. Electromagnetic Waves(0)
- 33. Geometric Optics(0)
- 34. Wave Optics(0)
- 35. Special Relativity(0)
2. 1D Motion / Kinematics
Graphing Position, Velocity, and Acceleration Graphs
2. 1D Motion / Kinematics
Graphing Position, Velocity, and Acceleration Graphs: Study with Video Lessons, Practice Problems & Examples
9PRACTICE PROBLEM
A train begins moving from rest at t = 0 along a straight track. The following table provides its position over different intervals of time. Find the acceleration of the train over each interval and represent it graphically.
![Table showing time in seconds and corresponding position in meters for a moving train.](data:image/png;base64,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)
A train begins moving from rest at t = 0 along a straight track. The following table provides its position over different intervals of time. Find the acceleration of the train over each interval and represent it graphically.