•Describe motion in terms of frame of reference•Express scalar and vector quantities•Understand the relationship between scalar and vector quantities

Motion• One-dimensional motion is the simplest form

of motion– A change in position– Motion that takes place in one direction- X or Y direction but not simultaneously

Motion takes place over time and depends upon the frame of reference•Frame of reference – a coordinate

system for specifying the precise

location of objects in space; a point that is

used to compare another objects motion

ScalarA SCALAR is ANY quantity in

physics that has MAGNITUDE, but NOT a direction associated with it; it has nothing to do with spacial direction

Magnitude – A numerical value with units.

Scalar Example

Magnitude

Speed 20 m/s

Distance 10 m

Age 15 years

Heat 1000 calories

VectorA VECTOR is ANY quantity in

physics that has BOTH MAGNITUDE and DIRECTION.

Vector Magnitude & Direction

Velocity 20 m/s, N

Acceleration 10 m/s/s, E

Force 5 N, West

Faxv,,,

Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

More about Vectors

• A vector is represented on paper by an arrow1. the length represents magnitude2. the arrow faces the direction of motion

Vectors can be added graphically

• Resultant – answer found by adding vectors

Vectors can be added graphically

The goal is to draw a mini version of the vectors to give you an accurate picture of the magnitude and direction. To do so, you must:

1. Pick a scale to represent the vectors. Make it simple yet appropriate.

2. Draw the tip of the vector as an arrow pointing in the appropriate direction.

3. Use a ruler & protractor to draw arrows for accuracy. The angle is always measured from the horizontal or vertical where the motion started.

• Vectors can be moved parallel to themselves in a diagram

• Vectors can be added in any order

• To subtract a vector, add its opposite

Vectors can be added graphically

Determining resultant magnitude• If the movement is in

straight lines that form a right triangle, Use the Pythagorean theorem to find the magnitude of the resultant

• Pythagorean Theorem for right triangles

d2 = x2 + y2

(Length of hypotenuse)2 = (length of one leg)2 + (length of the other leg)2

Determining resultant magnitude

Determining resultant magnitude

• To completely describe the resultant you also need to find the direction also

• When the resultant forms a right triangle, use the tangent function to find the angle (θ) of the resultant

Determining resultant direction

DETERMINING DIRECTION

B A

CD

N of E

N of W

S of W

S of E

• The angle (θ) of the resultant is the direction of the resultant

Determining resultant direction

Determining resultant direction

To find just the angle, use the inverse of the tangent function

• Remember when you solve for the displacement you are looking for the magnitude (d) and the direction (Θ with descriptor)

Kangaroos can easily jump as far as 8.0m. If a kangaroo makes five such jumps westward, how many jumps must it take northward to have a northwest displacement with a magnitude of 68m? What is the angle of the resultant displacement with respect to the north?

The emperor penguin is the best diver among birds: the record dive is 483m. Suppose an emperor penguin dives vertically to a depth of 483m and then swims horizontally a distance of 225m to the right. What angle would the vector of the resultant displacement make with the water’s surface? What is the magnitude of the penguin’s resultant displacement?