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Describing Motion

Describing Motion. in 3-D. (and 2-D). §3.1–3.2. Poll Question. Two objects can travel at the same speed but have different velocities. True False. Poll Question. Two objects can travel at the same velocity but have different speeds. True False. Vectors. Position is a vector

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Describing Motion

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

  2. Poll Question Two objects can travel at the same speed but have different velocities. • True • False

  3. Poll Question Two objects can travel at the same velocity but have different speeds. • True • False

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

  5. 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

  6. 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

  7. Change Vectors • Position and velocity may be in different directions • Velocity and acceleration may be in different directions q0 + Dq = qfDq = qf − q0

  8. Change Vectors • Position and velocity may be in different directions • Velocity and acceleration may be in different directions q0 + Dq = qfDq = qf − q0

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

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

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

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

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

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

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

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

  17. The component of aparallel to v causes the speed to change. • a|| = dv/dt • The component of aperpendicular to v causes the direction to change. • formula TBA (when we get to circular motion) Acceleration and Velocity

  18. Poll 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.

  19. A baseball thrown from the origin follows a path defined by r = 15 m/s ti + (15 m/s t – 5 m/s2t2) j. Board Work • Sketch its horizontal position, velocity, and acceleration vs. time. • x-t, vx-t, ax-t • Sketch its vertical position, velocity and acceleration vs. time. • y-t, vy-t, ay-t

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