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Describing Motion

Learn about vectors, velocity, and acceleration in describing motion in 3D and 2D. Understand the concepts of position, speed, magnitude, and components. Explore the relationship between velocity, acceleration, and direction in familiar situations. Test your knowledge with CPS questions.

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Describing Motion

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  1. Describing Motion in 3-D (and 2-D) §3.1–3.2

  2. Vectors • Position is a vector • Velocity is a vector • Acceleration is a vector

  3. A H B G C F D E CPS Question vi vf What is the direction of Dv?

  4. A H B G C F D E CPS Question vi vf What is the direction of Dv?

  5. A H B G C F D E CPS Question vi vf What is the direction of Dv?

  6. A H B G C F D E CPS Question vi What is the direction of Dv? vf

  7. A H B G C F D E CPS Question vi What is the direction of Dv? vf

  8. Velocity v = dr/dt • = dx/dt i+ dy/dt j + dz/dt k • = vxi + vyj + vzk • Acceleration a = dv/dt • = d2x/dt2i+ d2y/dt2j + d2z/dt2k • = axi + ayj + azk Describing 3-Vectors • Position r = x i + y j + z k

  9. Speed v = | v | = vx2 + vy2 + vz2 • Magnitude of accelerationa = | a | = ax2 + ay2 + az2 Magnitudes of 3-Vectors • Distance from origin r = | r | = x2+ y2+ z2

  10. Vectors • Position and velocity may be in different directions • Velocity and acceleration may be in different directions

  11. If a||v, path is straight. • If a||v, path is curved. Familiar Situations • Ballistic trajectories • Circular motion

  12. CPS Question If an object’s distance from the origin r does not change, its velocity must be zero. True. False.

  13. CPS Question If an object’s speed v does not change, its acceleration must be zero. True. False.

  14. The component of aparallel to v causes the speed to change. • The component of aperpendicular to v causes the direction to change. Acceleration and Velocity

  15. CPS Question The rate of change of an object’s speed d|v|/dt is the same as the magnitude of its acceleration |dv/dt|. Always. Sometimes. Never.

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