Distance and Displacement in Science

8
8
th
th
 Grade Science
 Grade Science
Chapter 11
Chapter 11
Distance and Displacement
Distance and Displacement
Learning Objectives
Learning Objectives
 
I can describe the difference between scalar and vector
quantities.
I can determine displacement and distance using a scale
diagram or calculation.
I can calculate the displacement of an object with two
vector quantities in one direction or at right angles.
Physics Introduction
Physics Introduction
 
The motion of objects can be described by words. Even
a person without a background in physics has a
collection of words that can be used to describe moving
objects. Words and phrases such as 
going fast,
stopped, slowing down, speeding up, and turning
provide a sufficient vocabulary for describing the motion
of objects. In physics, we use these words and many
more. We will be expanding upon this vocabulary list
with words such as (but not limited to) 
distance,
displacement, speed, velocity, and acceleration.
Scalars and Vectors
Scalars and Vectors
 
All physical quantities can be divided into two groups –
scalers and vectors
 
When determining if a quantity is a vector or a scaler
you need to ask 1 question, does direction matter?
 
Vector
 - quantity with both magnitude (size or
numerical value) and direction
Scalar
 - quantity with magnitude (size or numerical
value) only
Examples of Scalars and Vectors
Examples of Scalars and Vectors
 
Vectors
:
 Displacement
 Velocity
 Acceleration
 Momentum
 Force
 
Scalars:
 Distance
 Speed
 Time
 Mass
 Energy
Vectors
Vectors
 
Often represented by arrows.
Length of the arrow represents the magnitude (how
far, how fast, how strong, etc. depending on the type
of vector)
Do you know the difference?
Do you know the difference?
 
Scalar
 
Scalar
 
Scalar
 
Scalar
 
Vector
 
Vector
Distance
Distance
 
 
Distance (d) 
Distance (d) 
– how far an object travels or the
– how far an object travels or the
length of a path between 2 points.
length of a path between 2 points.
D
D
o
o
e
e
s
s
 
 
n
n
o
o
t
t
 
 
d
d
e
e
p
p
e
e
n
n
d
d
 
 
o
o
n
n
 
 
d
d
i
i
r
r
e
e
c
c
t
t
i
i
o
o
n
n
.
.
Scalar or vector quantity?
Scalar or vector quantity?
Measured with a ruler or meter stick
Measured with a ruler or meter stick
 
 
 
 
 
 
 
 
What 
What 
distance
distance
 did the ant travel?
 did the ant travel?
 
Scalar
Displacement
Displacement
 
Displacement (
Displacement (
x) 
x) 
–is the direction and the length of a
–is the direction and the length of a
straight line from the starting point to the ending point or
straight line from the starting point to the ending point or
where you are in relation to where you started from.
where you are in relation to where you started from.
Does
Does
 depend on direction. 
 depend on direction. 
Vector Quantity
Vector Quantity
Examples of directions:
Examples of directions:
+ and –
+ and –
N, S, E, W
N, S, E, W
Angles
Angles
Distance and Displacement
Distance and Displacement
 
Let’s visit our ant, and we we’ll find his
distance and displacement.
 
 
 
 
Distance: 3 cm
Displacement: +3 cm
The positive gives the ant a direction!
Distance and Displacement
Distance and Displacement
 
Find the ant’s  distance and displacement again.
Remember, displacement has direction!
 
 
 
 
 
Distance: 3 cm
Displacement: -3 cm
Distance and Displacement
Distance and Displacement
 
Find the distance and displacement of the
ant.
 
 
 
 
Distance: 7 cm
Displacement: +3 cm
Displacement and Distance in 2 Directions
Displacement and Distance in 2 Directions
 
You walk 3m east.
Than turn and go 4m North.
What is the distance of the walk?
 
Distance -
3m East
4m North
 
3m + 4m =
 
7m
Displacement and Distance in 2 Directions
Displacement and Distance in 2 Directions
You walk 3m east.
Than turn and go 4m North.
What is the displacement of
the walk?
Displacement -
3m East
4m North
 
5m NE
5
m 
North E
ast
Displacement vs. Distance
Displacement vs. Distance
 
Example of distance:
The ant walked 3 cm.
Example of displacement:
The ant walked 3 cm EAST.
An object’s distance traveled and its displacement aren’t
always the same!
Distance vs. Displacement
Distance vs. Displacement
You drive the path, and your odometer goes up
You drive the path, and your odometer goes up
by 8 miles (your distance).
by 8 miles (your distance).
Your displacement is the shorter 
Your displacement is the shorter 
directed
directed
distance from start to stop (green arrow).
distance from start to stop (green arrow).
start
stop
Distance and Displacement
Distance and Displacement
 
What is the distance of the entire trip?
What is the displacement of the entire trip?
 
3 + 3 = 6 miles
 
0 miles
Distance and Displacement
Distance and Displacement
 
What is the distance of the entire trip?
 
 
What is the displacement of the entire trip?
 
160 + 120 + 80
= 360m
 
120m East
Meters (m)
 
Distance start to A –
 
Total Distance –
 
Displacement -
 
11
cm
 
A
 
11cm
 
11cm
 
11cm N
11
cm
A
 
7cm
 
B
 
7cm
 
11cm + 7cm = 18cm
Big Ideas
Big Ideas
 
Vectors
 are quantities with both magnitude (size and
numerical value) and direction. An example is
displacement.
Scalers
 are quantities with just magnitude (size or
numerical value). An example is distance.
When 2 vectors are in the same direction you add them
and when they are in opposite directions you subtract
them.
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Exploring the concepts of distance and displacement in science, this content covers the difference between scalar and vector quantities, methods for determining displacement and distance, and examples of scalars and vectors. It also delves into the fundamental definitions of distance and displacement, showcasing how they are measured and their significance in physics.


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  1. 8thGrade Science Chapter 11 Distance and Displacement

  2. Learning Objectives I can describe the difference between scalar and vector quantities. I can determine displacement and distance using a scale diagram or calculation. I can calculate the displacement of an object with two vector quantities in one direction or at right angles.

  3. Physics Introduction The motion of objects can be described by words. Even a person without a background in physics has a collection of words that can be used to describe moving objects. Words and phrases such as going fast, stopped, slowing down, speeding up, and turning provide a sufficient vocabulary for describing the motion of objects. In physics, we use these words and many more. We will be expanding upon this vocabulary list with words such as (but not limited to) distance, displacement, speed, velocity, and acceleration.

  4. Scalars and Vectors All physical quantities can be divided into two groups scalers and vectors When determining if a quantity is a vector or a scaler you need to ask 1 question, does direction matter? Vector - quantity with both magnitude (size or numerical value) and direction Scalar - quantity with magnitude (size or numerical value) only

  5. Examples of Scalars and Vectors Scalars: Distance Speed Time Mass Energy Vectors: Displacement Velocity Acceleration Momentum Force

  6. Vectors Often represented by arrows. Length of the arrow represents the magnitude (how far, how fast, how strong, etc. depending on the type of vector)

  7. Do you know the difference? Category Quantity 5 m 30 m/sec, East 5 mi., North 20 degrees Celsius 256 bytes 4000 Calories Scalar Vector Vector Scalar Scalar Scalar

  8. Distance Distance (d) how far an object travels or the length of a path between 2 points. Does not depend on direction. Scalar or vector quantity? Measured with a ruler or meter stick Scalar

  9. Displacement Displacement ( x) is the direction and the length of a straight line from the starting point to the ending point or where you are in relation to where you started from. Does depend on direction. Vector Quantity Examples of directions: + and N, S, E, W Angles

  10. Distance and Displacement Let s visit our ant, and we we ll find his distance and displacement. - + 0 1 2 3 4 5 6 7 8 9 10 cm Distance: 3 cm Displacement: +3 cm The positive gives the ant a direction!

  11. Distance and Displacement Find the ant s distance and displacement again. Remember, displacement has direction! - + 0 1 2 3 4 5 6 7 8 9 10 cm Distance: 3 cm Displacement: -3 cm

  12. Distance and Displacement Find the distance and displacement of the ant. - + 0 1 2 3 4 5 6 7 8 9 10 cm Distance: 7 cm Displacement: +3 cm

  13. Displacement and Distance in 2 Directions You walk 3m east. Than turn and go 4m North. What is the distance of the walk? 3m + 4m = 7m Distance - 4m North 3m East

  14. Displacement and Distance in 2 Directions You walk 3m east. Than turn and go 4m North. What is the displacement of the walk? Pythagorean theory A2 + B2 = C2 32 + 42 = C2 9 + 16 = C2 25 = C2 25 = C 4m North 5m NE Displacement - 3m East

  15. Displacement vs. Distance Example of distance: The ant walked 3 cm. Example of displacement: The ant walked 3 cm EAST. An object s distance traveled and its displacement aren t always the same!

  16. Distance vs. Displacement You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (green arrow). start stop

  17. Distance and Displacement What is the distance of the entire trip? What is the displacement of the entire trip? 3 + 3 = 6 miles 0 miles

  18. Distance and Displacement 160 + 120 + 80 = 360m 120m East What is the distance of the entire trip? What is the displacement of the entire trip? Meters (m)

  19. A Distance start to A 11cm Total Distance 11cm 11 cm Displacement - 11cm N

  20. B A 7cm Distance A to B 7cm Total Distance 11cm + 7cm = 18cm 11 cm Displacement - A2 + B2 = C2 72 + 112 = C2 49 + 121 = C2 170 = C2 170 = C C = 13.04 NW

  21. Big Ideas Vectors are quantities with both magnitude (size and numerical value) and direction. An example is displacement. Scalers are quantities with just magnitude (size or numerical value). An example is distance. When 2 vectors are in the same direction you add them and when they are in opposite directions you subtract them.

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