General Physics 1
(Phys 110 : Mechanics)
CHAPTER 4
Motion in 2D and 3D
Phys
110
Chapter 4 : Motion in 2D and 3D
Revision :
2. Displacement vector (∆𝒓):
1. Position vector (𝒓):
𝒓 𝒕 = 𝒙 𝒕 𝒊 + 𝒚 𝒕 𝒋 + 𝒛(𝒕)𝒌
Particle’s
motion in
2D
Position
vector 1
Lesson 2 of 5
Slide 1
Position
vector 2
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 2 of 5
Slide 2
Objectives covered in this lesson :
1. to calculate the average velocity in magnitude-angle
Motion in 2D and 3D:
Average Velocity
notation and in unit-vector notation.
2. to calculate the instantaneous velocity in magnitude-
angle notation and write it in unit-vector notation.
Instantaneous Velocity
3. To specify that the direction of the instantaneous
velocity is always tangent to the particle's path, while
the direction of the average velocity is the same as the
direction of the displacement.
Phys
110
Chapter 4 : Motion in 2D and 3D
4-3 Average Velocity and Instantaneous Velocity :
Average Velocity (𝒗𝒂𝒗𝒈 ):
Q1: Does ∆𝒕 have a direction?
Q2: can ∆𝒕 be negative?
Q3: can we therefore determine the direction of 𝒗𝒂𝒗𝒈 ?
Lesson 2 of 5
Slide 3
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 2 of 5
Slide 4
4-3 Average Velocity and Instantaneous Velocity :
Average Velocity (𝒗𝒂𝒗𝒈 ):
Example: If a particle moves from its initial position to its final position in 2 seconds,
making a displacement
It’s average velocity will be:
Phys
110
Chapter 4 : Motion in 2D and 3D
4-3 Average Velocity and Instantaneous Velocity :
Instantaneous Velocity (or simply velocity) (𝒗):
Lesson 2 of 5
Slide 5
Phys
110
Chapter 4 : Motion in 2D and 3D
4-3 Average Velocity and Instantaneous Velocity :
Instantaneous Velocity
(or simply velocity) (𝒗):
To determine the
direction of 𝒗:
Lesson 2 of 5
Slide 6
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 2 of 5
Slide 7
4-3 Average Velocity and Instantaneous Velocity :
Instantaneous Velocity (or simply velocity) (𝒗):
BE CAREFUL :
In an (x, y, z) graph that shows the position (or path) of the
particle: the velocity vector is drawn to show the direction
of the velocity of the particle (which is located at its tail).
The magnitude of the velocity can be drawn in any scale
(not necessarily the scale of which the position vectors are
drawn) i.e. we cannot relate the velocity components to the x, y, and z axes in such a graph.
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 2 of 5
Slide 8
4-3 Average Velocity and Instantaneous Velocity :
Answer: (a) first, (b) third.
Phys
110
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-3) :
Lesson 2 of 5
Slide 9
Phys
110
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-3) :
Lesson 1 of 5
Slide 10
Phys
110
Lesson 2 of 5
Slide 11 (last)
Chapter 4 : Vectors
Summary:
Motion in 2D and 3D:
Next lesson we will cover:
Average velocity in 2D and 3D.
Section (4-4).
Instantaneous velocity in 2D and 3D.
Sample problem (4-4).
Sample problem (4-5).
Any Questions?