1. Displacement

2. Defining Position Position has three properties:
Origin, magnitude, direction
1 dimension
12 feet above sea level.
Origin: sea level
Magnitude: 12 feet
Direction: up
2 dimensions
65 miles west of Chicago.
Origin: downtown Chicago
Magnitude: 65 miles
Direction: west
3 dimensions
Range 200 m, bearing 270, at 30 altitude.
Origin: observer
Magnitude: 200 meters
Direction: 270 by the compass and 30 up.

3. Position Graph Position can be displayed on a graph.
The origin for position is the origin on the graph.
Axes are position coordinates.
The position is a vector.
A set of position points connected on a graph is a trajectory.
trajectory y
position vector x
2-dimensions (x, y)

4. Scalar Multiplication
A vector can be multiplied by a scalar.
Change feet to meters.
Walk twice as far in the same direction.
Scalar multiplication multiplies each component by the same factor.
The result is a new vector, always parallel to the original vector.

5. Reference Point Displacement is different from position trajectory
Position is measured relative to an origin common to all points.
Displacement is measured relative to the object’s initial position.
The path (trajectory) doesn’t matter for displacement.
position
origin

6. Displacement Vector The position vector is often designated by .
A change in a quantity is designated by Δ (delta).
Always take the final value and subtract the initial value. y x

7. Two Displacements
A hiker starts at a point 2.0 km east of camp, then walks to a point 3.0 km northeast of camp. What is the displacement of the hiker?
Each individual displacement is a vector that can be represented by an arrow.
3.0 km
2.0 km

8. Vector Subtraction
To subtract two vectors, place both at the same origin.
Start at the tip of the first and go to the tip of the second.

9. Component Subtraction
Multiplying a vector by -1 will create an antiparallel vector of the same magnitude.
Vector subtraction is equivalent to scalar multiplication and addition.

10. Displacement Components
Find the components of each vector, and subtract.
Ax = 2.0 km
Ay = 0.0 km
Bx = (3.0 km)cos45 = 2.1 km
By = (3.0 km)sin45 = 2.1 km
Dx = Bx – Ax = 0.1 km
Dy = By – Ay = 2.1 km