1. Motion

2. Motion must be described relative to something else.
What is Motion?
When a body is continuously changing its position with respect to the surroundings, we say that the body is in motion.
Motion must be described relative to something else.
Earth is the most common frame of reference.

3. Representing Motion
When studying motion, a starting point, called the origin must be identified.
The origin is the point at which all the variables have the value of zero.
The location of an object is called its position.
An object can have a negative position based on its origin.

4. Vectors and Scalars
Scalars are quantities that have magnitude (a number) only.
Vectors are quantities that have both a magnitude (size) and a direction.
Direction can be north, south, east, west, etc.

5. Distance is a Scalar Quantity
A measure of the length of a path an object takes in moving from one position to another is called distance. (How much ground has been covered?)
Distance is measured in meters.

6. Displacement is a Vector
Displacement is the overall change in an objects position. How far out of place is the object?
Determined by drawing a straight line from starting position to ending position
Is not always equal to distance traveled.

7. Displacement

8. Displacement is ZERO

9. Displacement
d = df- di
final position - initial position

10. Learning Check
Classify each of the following as either a vector or a scalar
A temperature of 98.6°C
A kilogram of flour
A ten yard penalty
Winds east at 20 knots
2 m
4 m

11. Representing Vectors http://www.nbclearn.com/nhl
Vector quantities are represented with arrows.
The length of the arrow should be drawn proportional to the magnitude of the quantity being represented.
The direction of the arrow should represent the direction of the quantity being represented.

12. Adding Vectors
A vector that represents the sum of the individual (component) vectors is called the resultant vector.
The resultant always points from the tail of the first vector to the tip of the last vector.
If two vectors are along the same plane and in the same direction they add together to produce a larger vector.
If two vectors are along the same plane and in opposite directions they add together to produce a smaller vector.

13. Example 1
Chris is flying his plane due East at 100 m/sec. A tailwind of 50 m/sec East pushes Chris’s plane. What is Chris’s resultant speed and direction?
Draw a Vector to represent each motion in the problem:
The plane moves due East at 100 m/sec.
A tailwind pushes the plane at 50 m/sec
Resultant includes both vectors added together

14. Example 2 Distance = 80 m Displacement = 20 m, North
Suppose a runner jogs north to the 50-m mark and then turns around and runs back south 30-m.
What is the total distance?
What is the total displacement?
North, 50 m South, 30 m
Distance = 80 m
Displacement = 20 m, North

15. Vector Addition
When two vectors in opposite planes are used to describe motion, the vectors can also be added head to tail.
These vectors will make a right angle with one another.
The resultant vector will be the hypotenuse of a right triangle.

16. Example 3
Eric leaves the base camp and hikes 11 km, east and then hikes 11 km north. Determine Eric's resulting displacement.

17. Vector Addition- Step 1 Connect the two vectors HEAD to TAIL To . . .
From . . .
11 km N
11 km, E
11 km N
11 km, E

18. STEP 2
Connect the start of the first vector to the tip of the second vector

19. Solving for the Resultant Vector
Use GEOMETRY to solve for the magnitude of the vector
Pythagorean Theorem

20. Example 4
Mandy walks 95 m east and then 55 m north. Graphically and mathematically solve for Mandy’s displacement.
Measure this distance
55 m, north
95 m, east

21. Example 4 Answer

22. Example 5
Suppose a hiker travels 10 km west, then 5 km south. Find the hiker’s displacement.

23. Example 5
Suppose a hiker travels 10 km west, then 5 km south. Find the hiker’s displacement.