Distance
and
Displacement
Chapter 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
20km
0
10
30km
20
30
15km
40
50
60
70
80
Displacement = 20 km + 30 km + 15 km = 65 km east
30km
0
10
20
-10km
30
30km
40
50
60
Displacement = 40 km + -10 km + 40 km = 70 km east
70
80
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.
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?
4m + 2m + 4m + 2m = 12m
– What is the total displacement?
Displacement = 0m
4m
2m
2m
4m
Speed
and
Velocity
Chapter 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?
Acceleration
Chapter 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
Time
a = v f – 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?