 # Distance and Displacement

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Distance and Displacement
Chapter 11.1

Key Concepts and Vocabulary
What is needed to describe motion completely? How are distance and displacement different? How do you add displacements? Vocabulary: Frame of Reference Relative Motion Distance Vector Resultant Vector

Distance Length of a path between two points.
Units: kilometers, meters, centimeters

Displacement Direction from the starting point and the length of a straight line from the starting point to the ending point.

Displacement Along A Straight Line
20km 30km 15km 10 20 30 40 50 60 70 80 Displacement = 20 km + 30 km + 15 km = 65 km east -10km 30km 30km 10 20 30 40 50 60 70 80 Displacement = 40 km km + 40 km = 70 km east

Vector Vector is a quantity that has magnitude and direction
12 km northwest Magnitude – size, length, or amount Length of arrows shows the magnitude

Displacement That Isn’t Along a Straight Line
When two or more displacement vectors have different directions, they can be combined by graphing.

Based on the red arrows, how far did Mrs. Ewald walk?
Add the magnitudes of each vector along the path. 2 long blocks south 2 short blocks east 1 long block south 3 short blocks east Total = 8 blocks or 11 short blocks Path walked by Mrs. Ewald 1 long block = 2 short blocks

Based on the red arrows, how far did Mrs. Ewald walk?
The vector in yellow is the resultant vector – vector sum of two or more vectors. Points directly from start to finish. Resultant vector = 8 short blocks Path walked by Mrs. Ewald

Question? Mrs. Ewald walks 4m east, 2m south, 4m west, and 2m north.
What is the total distance Mrs. Ewald walked? What is the total displacement? 4m + 2m + 4m + 2m = 12m Displacement = 0m 2m 4m

Speed and Velocity Chapter 11.2

Key Concepts and Vocabulary
How is instant speed and average speed different? How are speed and velocity different? Vocabulary: Speed Average Speed Instantaneous Speed Velocity

Speed Ratio of the distance an object moves to the amount of time the object moves. Equations:

Velocity The speed and direction an object is moving relative to a reference point. Equations:

Example A car travels 85 km from Town A to Town B, then 45 km from Town B to Town C. The total trip took 1.5 hours. What was the average speed of the car?

Example A bicyclist travels for 1.5 hours at an average speed of 32 km/h. How far does the bicyclist travel in that time?

Example A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometers in 16 minutes. What is the joggers average speed in kilometers per minute?

Example A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average speed?

Acceleration Chapter 11.3

Key Concepts and Vocabulary
How are changes in velocities described? How can you calculate acceleration? Vocabulary: Acceleration Free Fall

Acceleration A vector described as a changes in speed, changes in direction, or changes in both. Change in Speed Free fall (9.8 m/s2) Change in Direction Riding a merry-go-round Changes in Speed and Direction Speeding up around a corner

Calculating Acceleration
Equation: Acceleration = Change in Velocity Time Acceleration = Velocityfinal – Velocityinitial a = vf – vi t Unit of Measure: m/s2, km/s2

Example A car travelling at 10 m/s starts to slow down steadily. It comes to a complete stop in 20 seconds. What is its acceleration?

Example An airplane travels down a runway for 4.0 seconds, with an acceleration of 9.0 m/s2. What is its change in velocity during this time?

Example A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water?

Example A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boys hand?