Transcript PPT

More Practice: Distance, Speed,
and Unit Conversion
More Practice: Distance, Speed,
and Unit Conversion
More Practice: Distance, Speed,
and Unit Conversion
More Practice: Distance, Speed,
and Unit Conversion
More Practice: Distance, Speed,
and Unit Conversion
More Practice: Distance, Speed,
and Unit Conversion
More Practice: Distance, Speed,
and Unit Conversion
Vectors: Displacement and
Velocity: Learning Goals


The student will be able to distinguish between
distance and displacement and speed and
velocity. (B2.1)
The student will be able to distinguish between
constant, instantaneous, and average speed and
give examples of each involving uniform and
non-uniform motion . (B3.1)
Vectors: Displacement
and Velocity
SPH4C
Vectors
A vector quantity has both magnitude and
Vectors
A vector quantity has both magnitude and direction.
Vectors
A vector quantity has both magnitude and direction.
The direction is given in square brackets after the
units:
Vectors
A vector quantity has both magnitude and direction.
The direction is given in square brackets after the
units:
e.g.,
5 km [West]
Vectors
Examples of vectors:
 displacement
 velocity
Vectors
Examples of vectors:
 displacement
 velocity
 acceleration
Vectors
Examples of vectors:
 displacement
 velocity
 acceleration
 force
 etc.
Displacement
Displacement is how far an object
is from its starting position and
is not simply distance travelled
+ a direction.

d
Displacement
Displacement is how far an object
is from its starting position and
is not simply distance travelled
+ a direction.
E.g., the distance travelled here by
a driver commuting from
Manhattan to N.J. was 14.5 km
even though the displacement
was only 2.7 km [North].

d
Displacement
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West]. What was her distance travelled?
What was her displacement?
Displacement
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West]. What was her distance travelled?
What was her displacement?
Distance travelled: d = 2 m + 1 m = 3 m
Displacement
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West]. What was her distance travelled?
What was her displacement?
Distance travelled: d = 2 m + 1 m = 3 m
2m
Displacement:
1m
Displacement
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West]. What was her distance travelled?
What was her displacement?
Distance travelled: d = 2 m + 1 m = 3 m
2m
Displacement:
1m
1m
She is 1 m [East] of her original starting position.
Displacement
2m
1m
1m
We can represent [East] as the positive direction
and [West] as the negative direction:
Displacement
2m
1m
1m
We can represent [East] as the positive direction
and [West] as the negative direction:

d = 2 m [East] + 1 m [West]
=+2m–1m
Displacement
2m
1m
1m
We can represent [East] as the positive direction
and [West] as the negative direction:

d = 2 m [East] + 1 m [West]
=+2m–1m
=+1m
Displacement
2m
1m
1m
We can represent [East] as the positive direction
and [West] as the negative direction:

d = 2 m [East] + 1 m [West]
=+2m–1m
=+1m
= 1 m [East]
Directions
It is conventional to represent the following
directions as positive:
 forward
Directions
It is conventional to represent the following
directions as positive:
 forward
 right
Directions
It is conventional to represent the following
directions as positive:
 forward
 right
 up
Directions
It is conventional to represent the following
directions as positive:
 forward
 right
 up
 North
 East
Velocity
Velocity is similarly not simply speed + a direction.
Velocity
Velocity is similarly not simply speed + a direction.

vavg

d

t
Velocity
Velocity is similarly not simply speed + a direction.

vavg

d

t
displaceme nt
average velocity 
time
Velocity
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West] in 3 s. What was her average speed?
What was her average velocity?
Velocity
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West] in 3 s. What was her average speed?
What was her average velocity?
vavg
d 3 m


 1 ms
t 3 s
Velocity
Example: Ms. Rosebery walks 2 m [East] and then
1 m [West] in 3 s. What was her average speed?
What was her average velocity?
d 3 m
vavg 

 1 ms
t 3 s


d 1m[ East]
vavg 

 0.3 ms [ East]
t
3s
Instantaneous Velocity
Average velocity is rarely calculated for an object
changing direction. It makes more sense to talk
about the instantaneous velocity, which is the
speed + the direction at that particular instant.
Instantaneous Velocity
Average velocity is rarely calculated for an object
changing direction. It makes more sense to talk
about the instantaneous velocity, which is the
speed + the direction at that particular instant.
Instantaneous Velocity
Assuming Ms. Rosebery walked at constant speed,
what was her instantaneous velocity at:
1.5 s?
2 s?
2.5 s?
Instantaneous Velocity
Assuming Ms. Rosebery walked at constant speed,
what was her instantaneous velocity at:
1.5 s? 1 m/s [East]
2 s?
2.5 s?
Instantaneous Velocity
Assuming Ms. Rosebery walked at constant speed,
what was her instantaneous velocity at:
1.5 s? 1 m/s [East]
2 s? 0 m/s (while she is changing direction)
2.5 s? 1 m/s [West]
Instantaneous Velocity
Assuming Ms. Rosebery walked at constant speed,
what was her instantaneous velocity at:
1.5 s? 1 m/s [East]
2 s? 0 m/s (while she is changing direction)
2.5 s?
More Practice
More Practice: Displacement and Velocity
and Graphing Motion