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Position and
displacement
Objectives
- Describe motion in 1D using position, distance, and displacement.
- Analyze motion in 1D using position, distance, and displacement.
- Correctly use and interpret positive and negative values of position and displacement.
- A robot car moves 200 m east, turns around and moves 600 m west. Describe this motion using position, displacement, and distance.
- A woman starts at x = -10 m and has three successive displacements of -5 m. What is her final position?
- What displacement moves an object from a position of 25 meters to a position of -15 meters?
Assessment Physics terms
- origin
- position
- displacement
Equations
The final position equals the initial position plus any displacements.
Describing motion
Before you can predict an object’s motion, you need to be able to describe it. How do we describe an object’s position? If the object moves, what is the difference between its distance and displacement?
Exploring the ideas
Click on this interactive on page 74.
Engaging with the concept
Initial position or final position can be entered here. Enter a displacement of 5 meters Click [Enter] 5
Engaging with the concept
Final position Distance moved 5
Engaging with the concept
5 5 Add a displacement of -10 meters 5 -10^5
Engaging with the concept
5 Click [Enter] Distance moved Final position 15
Engaging with the concept
-10^5
Importance of the origin
GPS systems use 0° latitude and longitude as the origin. Position tells you where you are relative to an origin. Positive and negative values tell you whether you are in front or behind, or to the left or right of the origin.
Position
The position equation
The final position equals the initial position plus any displacements. How is displacement described?
Coordinate systems
To describe displacement, you must create a coordinate system and choose which direction is positive and which is negative. This is a choice! It may change for different problems.
- (^) + Left - Right West - East
Up Down North South
Displacement
Displacement is a change in position. Positive and negative values indicate direction.
Displacement is a vector
Displacement is a vector because it contains direction information. For motion along a line, direction is positive or negative.
Distance is a scalar
Distance is a scalar quantity. It does not include direction information.
Adding displacements
An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position? Add displacements graphically by drawing vectors to scale:
- The first vector starts at the initial position.
- The second vector starts at the end of the first vector.
Adding displacements
An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position?
Adding displacements
An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position? You can also use numerical addition. This is faster and more accurate.
Problem solving
How do you recognize the initial position and displacements? What do you choose as the initial position? Example: “A boat sails 50 km north then 800 km south. What is the sailboat’s final position?” How do you recognize the initial position and displacements? What do you choose as the initial position? Example: “A boat sails 50 km north then 800 km south. What is the sailboat’s final position?”
Problem solving
Let the initial position be zero km: When nothing is said to establish a particular start you may assume the initial position is zero.
- A woman starts at x = -10 m and has three successive displacements of -5 m. What is her final position? The final position is -25 m.
Assessment
- What displacement moves an object from a position of 25 meters to a position of -15 meters?
Assessment
Asked: displacement Given: initial and final positions Answer: Relationships: Solution:
- What displacement moves an object from a position of 25 meters to a position of -15 meters? Asked: displacement Given: initial and final positions
Relationships: xf = xi + d
Solution: d = xf – xi
d = -15 m – 25 m = -40 m
Assessment
Answer: The displacement is -40 meters
