5. One-Dimensional Kinematics: Non-Constant Acceleration

• Course Home
• Syllabus
• Introduction to Mechanics

  • 1. Units and Dimensional Analysis
  • 2. Problem Solving and Estimation
• Mathematics: The Language of Science

  • 3. Cartesian Coordinates and Vectors
• Translational Kinematics

  • 4. One-Dimensional Kinematics and Free Fall
  • 5. One-Dimensional Kinematics: Non-Constant Acceleration
  • 6. Two-Dimensional Kinematics
• Force and Newton's Laws of Motion

  • 7. Concept of Force
  • 8. Applications of Newton's Second Law
• Circular Motion

  • 9. Circular Motion Kinematics
  • 10. Circular Motion Dynamics
• Conservation of Energy

  • 11. Work and Energy
  • 12. Work and the Dot Product
  • 13. Potential Energy
  • 14. Application of Energy Conservation
  • 15. Mechanical Energy and the Simple Harmonic Oscillator
• Momentum

  • 16. Momentum and Impulse
  • 17. Systems, Center of Mass, and Conservation of Momentum
  • 18. Collision Theory
  • 19. Continuous Mass Flow
• Two-Dimensional Rotational Motion

  • 20. Two-Dimensional Rotational Kinematics
  • 21. Two-Dimensional Rotational Dynamics
  • 22. Torque and the Simple Harmonic Oscillator
  • 23. Static Equilibrium
• Angular Momentum

  • 24. Angular Momentum
  • 25. Conservation of Angular Momentum
• Rotation and Translation

  • 26. Two-Dimensional Rotation and Translation Kinematics
  • 27. Two-Dimensional Rotation and Translation Dynamics
• Central Force Motion

  • 28. Central Force Motion and the Kepler Problem
• Download Course Materials

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Learning Objectives

• Explain the concepts of position, velocity and acceleration for different kinds of motion, and be able to differentiate and integrate mathematical functions describing them.
• Describe the different kinds of one-dimensional motion using models such as constant, harmonic and exponential acceleration models.

Preparation

Course Notes

Notes: Integration and Kinematics (PDF - 1.6MB)

Suggested Textbook Reading (Optional)

Chapter 2.6. Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky's University Physics: with Modern Physics. 12th ed. San Francisco, CA: Addison-Wesley, 2007. ISBN: 9780805321876.

Learning Activities

Guided Activities

Read through the class slides carefully. They explain all of the concepts from the module.

Slides: One-Dimensional Kinematics, Non Constant Acceleration (PDF)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems. If you are struggling with the Challenge Problems, watch the Homework Help Session videos, which will give you tips on how to tackle problems of this type.

Concept Questions

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF - 2.6MB)

Solutions (PDF)

Problem Solving Help

In the following video Prof. Walter Lewin explains how to approach the Challenge Problems.

Help Session

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Related Resources

There are countless resources available online to help you learn physics. Try these:

• Try a couple interactive simulations from PhET:
  • Calculus Grapher
  • The Moving Man
• Learn about acceleration from HyperPhysics at Georgia State University.

 

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