Download presentation
Presentation is loading. Please wait.
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
Describing 3-Vectors Position r = x i + y j + z k Velocity v = dr/dt
= dx/dt i + dy/dt j + dz/dt k = vx i + vy j + vz k Acceleration a = dv/dt = d2x/dt2 i + d2y/dt2 j + d2z/dt2 k = ax i + ay j + az k
6
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
7
Change Vectors Position and velocity may be in different directions
Velocity and acceleration may be in different directions q0 + Dq = qf Dq = qf − q0
8
Change Vectors Position and velocity may be in different directions
Velocity and acceleration may be in different directions q0 + Dq = qf Dq = qf − q0
9
Quick Question vi vf What is the direction of Dv? A B C D E F G H
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
Familiar Situations Ballistic trajectories Circular motion
If a || v, path is straight. If a || v, path is curved.
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
Acceleration and Velocity
The component of a parallel to v causes the speed to change. a|| = dv/dt The component of a perpendicular to v causes the direction to change. formula TBA (when we get to circular motion)
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
r = 15 m/s t i + (15 m/s t – 5 m/s2 t2) j.
Board Work A baseball thrown from the origin follows a path defined by r = 15 m/s t i + (15 m/s t – 5 m/s2 t2) j. 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
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.