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 3 of 5
Slide 1
Position
vector 2
Phys
110
Chapter 4 : Motion in 2D and 3D
Revision :
3. Average Velocity (𝒗𝒂𝒗𝒈 ):
direction of 𝒗𝒂𝒗𝒈 = direction of ∆𝒓
Lesson 3 of 5
Slide 2
4. Instantaneous Velocity (Velocity) (𝒗):
direction of 𝒗 : along
the tangent to path
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 3 of 5
Slide 3
Objectives covered in this lesson :
Motion in 2D and 3D:
1. to calculate the average acceleration and its
Average Acceleration
Instantaneous Acceleration
direction.
2. to calculate the instantaneous acceleration
and its direction.
Phys
110
Chapter 4 : Motion in 2D and 3D
4-4 Average Acceleration and Instantaneous Acceleration :
Average Acceleration (𝒂𝒂𝒗𝒈 ):
Lesson 3 of 5
Slide 4
Phys
110
Chapter 4 : Motion in 2D and 3D
4-4 Average Acceleration and Instantaneous Acceleration :
Instantaneous Acceleration (or simply Acceleration) (𝒂):
Lesson 3 of 5
Slide 5
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 3 of 5
Slide 6
4-4 Average Acceleration and Instantaneous Acceleration :
Instantaneous Acceleration (𝒂):
To determine its direction:
use the:
acceleration components,
or its magnitude and angle,
to draw it separately,
then shift it so that its tail is
on the particle’s position.
Unlike the direction of the velocity (which is tangent to the path), the acceleration
vector’s direction does not have any specific relationship with the path.
Phys
110
Chapter 4 : Motion in 2D and 3D
4-4 Average Acceleration and Instantaneous Acceleration :
Lesson 3 of 5
Slide 7
Phys
110
Chapter 4 : Motion in 2D and 3D
Lesson 3 of 5
Slide 8
4-4 Average Acceleration and Instantaneous Acceleration :
Answer: take second derivative with respect of time:
(1) and (3) : 𝑎𝑥 and 𝑎𝑦 are constant  𝑎 is constant.
(2) and (4) : 𝑎𝑦 is constant, but 𝑎𝑥 is not  𝑎 is not constant.
Phys
110
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-4) :
Lesson 3 of 5
Slide 9
Phys
110
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-4) :
Lesson 3 of 5
Slide 10
Phys
110
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-5) :
Lesson 3 of 5
Slide 11
Phys
110
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-5) :
Lesson 3 of 5
Slide 12
Phys
110
Lesson 3 of 5
Slide 13 (last)
Chapter 4 : Vectors
Summary:
Next lesson we will cover:
Motion in 2D and 3D:
Section (4-5).
Average acceleration in 2D and 3D.
Section (4-6).
Instantaneous acceleration in 2D and 3D.
Problem 21.
Problem 38.
Sample problem (4-7).
Any Questions?