Dr Pusey
Learning Outcomes
Distinguish between Distance and Displacement when
comparing positions
Distinguish between Scalar and Vector Quantities
Add and subtract vectors in one and two dimensions
What are 1, 2 and 3 dimensional
space?
 Think of it like this:
 1 Dimensional (1D) - sideways
 2 Dimensional (2D) - sideways
and upwards
 3 Dimensional (3D) – sideways,
upwards and into!
Vectors and Scalars
 Scalars
 ‘Magnitude’ only
 Examples
 Distance (20 m)
 Speed (10 m/s)
 Mass (30 kg)
 Vectors
 ‘Magnitude’ AND direction
 Examples
 Displacement (20 m North)
 Velocity (10 m/s Eastwards)
 Weight (20 N Downwards)
No Joke! – Weight is a Force, Forces are Vectors
Check your understanding
Example
5m
30 m/s, East
5 km, North
20 degrees Celsius
256 bytes
4000 Calories
Scalar or Vector?
Check your understanding
Example
Scalar or Vector?
5m
This is a scalar; there is no
direction listed for it.
5 km, North
This is a vector; a direction is listed
for it.
30 m/s, East
20 degrees Celsius
256 bytes
4000 Calories
This is a vector; a direction is listed
for it.
This is a scalar; there is no
direction listed for it.
This is a scalar; there is no
direction listed for it.
This is a scalar; there is no
direction listed for it.
Examples of Scalars and Vectors
Mass
Momentum
Velocity
Weight
Work
Scalar
Length
Distance
Displacement
Speed
Velocity
Power
Energy
Acceleration
Force
Friction
Vector
Examples of Scalars and Vectors
Scalar
Vector
Mass
Length
Distance
Speed
Power
Energy
Work
Displacement
Velocity
Acceleration
Force
Weight
Friction
Momentum
Distance vs Displacement
 Distance is a scalar quantity that refers to ‘how much
ground an object has covered’ during its motion.
 Displacement is a vector quantity that refers to ‘how
far out of place an object is’; it is the object's overall
change in position.
Adding Vectors
Example 1
A student walks 5 m forwards and then 5 m backwards.
 What distance did she travel?
 What is her displacement?
Adding Vectors
Example 1
A student walks 5 m forwards and then 5 m backwards.
 What distance did she travel?
5 m + 5 m = 10 m
 What is her displacement?
0m
5m
5m
Distance and Displacement
 Distance: The total path
 Displacement: The difference in position from the
start
http://thescienceclassroom.org/physics/motion-in-1-d/distance-and-displacement/
Position, Distance, Displacement
Home
7 km
School 
6 km
A student walks to the Beach for a quick surf in the
morning and then back to School to start his day.
• A) What distance did he travel?
• B) What is his displacement?
Beach
3 km
Cinemas
Position, Distance, Displacement
Home
7 km
Displacement
School 
Distance
6 km
Distance
Beach
3 km
• A) What distance did he travel? 7+6+6 = 19km
• B) What is his displacement? 7km East
Cinemas
Position, Distance, Displacement
Home
7 km
School 
6 km
• He then decides to go and watch the latest
vampire / goth movie with his mates after school.
Beach
3 km
• What is the total distance travelled?
• What is the displacement of the student?
• Total: HOME  BEACH  SCHOOL  CINEMAS
Cinemas
Position, Distance, Displacement
Home
7 km
• Distance:
Beach (13km)
+School (6km)
+Cinema (6.7km)
• = 25.7km
School 
6 km
62
32
+
=6.7km
Beach
3 km
Displacement: Vector Addition
Home
7 km
School 
• Displacement
= 13.3 km SOUTH-EAST
6 km
132 + 32
=13.3 km
Beach
3 km
HELP! LOST DRONE!
Dr Pusey’s SupaTEK Drone’s GPS has failed and we are
trying to work out where it currently is so we can give
co-ordinates to bring it home! The telemetry data shows
the following sequence of vectors:
7km North  4km East  3km South  8km West
What two vectors would bring the drone home?
MEGA BONUS POINTS – What ONE vector would bring
the drone home?
HELP! LOST DRONE!
7km North  4km East  3km South  8km West
First: Stack the vectors up (head to toe) and draw the
“RESULTANT VECTOR” – This is the Displacement
Vector
4km
8km
Resultant Vector
7km
3km
HELP! LOST DRONE!
Work out how far North and East the drone is using graph
paper. OR, Simply add up the North and East components
separately.
7km – 3km = 4 km North
4km – 8km = -4 km East = 4 km West
4km
8km
Resultant Vector
7km
2km
4km
4km
Bring it home…
2 Vectors to Return:
=4km East and 4km South
1 Vector to Return:
=5.66 km South-East
4km
= 42 + 42
= 5.66 km
4km
How did you go?
 Distinguish between Distance and Displacement when
comparing positions
 Distinguish between Scalar and Vector Quantities
 Add and subtract vectors in one and two dimensions