Distance and Displacement

Distance and

DisplacementChapter 11.1

Key Concepts and Vocabulary• Key Concepts:– 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

0 10 20 30 40 50 60 70 80

20km 30km 15km

Displacement = 20 km + 30 km + 15 km = 65 km east

0 10 20 30 40 50 60 70 80

30km 30km-10km

Displacement = 40 km + -10 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

Vector Addition Problems

Displacement That Isn’t Along a Straight Line

• When two or more displacement vectors have different directions, they can be combined by graphing.

Path walked by Mrs. Ewald

Add the magnitudes of each vector along the path.

2 long blocks south2 short blocks east1 long block south3 short blocks eastTotal = 8 blocks or 11 short blocks

Based on the red arrows, how far did Mrs. Ewald walk?

1 long block = 2 short blocks

Path walked by Mrs. Ewald

•The vector in yellow is the resultant vector – vector sum of two or more vectors.•Points directly from start to finish.

Based on the red arrows, how far did Mrs. Ewald walk?

Resultant vector = 8 short blocks

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?

2m2m

4m

4m

4m + 2m + 4m + 2m = 12m

Displacement = 0m

Speed and

VelocityChapter 11.2

Key Concepts and Vocabulary• Key Concepts:– 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?

AccelerationChapter 11.3

Key Concepts and Vocabulary• Key Concepts:– 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

Timea = 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?