1. Describing Motion
in 3-D
(and 2-D)
§3.4–3.5

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

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

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

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

6. Position and Displacement
Position is where something is
r = (x, y, z)
Displacement is change in position
Dr = (Dx, Dy, Dz) = Dxx + Dyy + Dzz
Distance is the magnitude of displacement.

7. Velocity and Acceleration
Velocity v = rate of change of r
average vavg = Dr/Dt
t is scalar; vavg and Dr are same direction
instantaneous v = lim Dr/Dt
Dt   0
Speed is the magnitude of velocity.
Acceleration a = rate of change of v
Average aavg = Dv/Dt
instantaneous a = lim Dv/Dt
Dt   0

8. Describing 3-Vectors Position r = x x + yy + zz Velocity v = Dr /Dt
= Dx/Dt x + Dy/Dt y + Dz/Dt z
= vx x + vy y + vzz
Acceleration a = Dv/dt
= ax x + ayy + azz

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

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

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

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

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

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

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

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

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

18. Acceleration and Velocity
The component of a parallel to v causes the speed to change.
The component of a perpendicular to v causes the direction to change.

19. Question
The rate of change of an object’s speed is the same as the magnitude of its acceleration.
Always.
Sometimes.
Never.