12.1
• Distance is the space between two
points, commonly measured in
metres (m).
• Distances between two points can
depend on the path taken.
• Time (t) is the duration of an event.
• Time is often referred to as a time interval and given the
symbol t.
DO QUESTIONS 1-7 pg. 345 CYU
VOCABULARY
time interval
slope
Answers 12.1-CYU #1-7
1. A. Year, B. Minute, C. second D. Hour E. Day or week or
Month
2. Distance is the length of the path along which an object
moves
3. The distance would be difficult to measure again
4. Y is shorter, x is 2200 m long and y is 1655 m long therefore
545 m shorter
5. A time interval is the difference between an ending time and
a starting time
6. 2820 s
7. Starting time and ending time are needed to measure a time
interval
• A period (T ) is the time interval
between two repeating events,
such as a pendulum swinging.
• It is related to frequency as:
Read Sample Problem #1 p. 343 then
DO CYU #8-10 p. 345
Answers 2.1-CYU #8-10
8. T = 0.25 s; f= 4 Hz
9. T = 2.8 s; f=0.36 Hz
10. T = 0.005 s
Next Day – you will be gathering data for a
two part lab
1. Determine the Length
of a Pendulum with a
Period of one Second
2. Does the mass of the
Pendulum effect the
Period
12.2
• By relating time and distance, we can determine
speed, which is the distance an object travels (d) divided by
the time interval (t).
• The average speed of an object is the total distance the object
travelled divided by the total time taken.
• Instantaneous speed is the speed of an object at a particular
instant in time.
• For example, a car speedometer reads instantaneous speed.
• For an object travelling at a constant speed (i.e. uniform
motion), the average speed is equal to its instantaneous speed.
VOCABULARY
speed
average speed
instantaneous speed
Graphs are used to
illustrate the
mathematical
relationships of two
quantities.
***Be sure to really
think about what
the graph ACTUALLY
represents***
Recall x is always the independent variable and y is the dependant variable
12.3
Graphing Distance and Time
• A distance–time graph has
distance on the y-axis and
time on the x-axis.
• The slope of a line on a distance–
time graph is equal to average speed.
• The units for the slope would be
metres/second (m/s), the same as
speed.
Do CYU 12.2 p. 350
CYU 12.2 Answers #1-14
1.
2.
A. 1.7 m/s B. 0.55 m/s C. 0.82 m/s
VAV for the trip was 56 km/h ; VAV while the car was
moving was 96 km/h
3. 19.1 m/s
4. A. 113 cm. B. 113 cm/m or 1.9 cm/s C. Yes, the
instantaneous speed is not changing
5. 1.7 s
12. A. About 42000 km B. 1.5 h
6. 0.44 s
7. 6.1 x 10-3 s
13. The average speed of object can change over
8. 4.0 x 102 m
time. It depends only on the distance travelled and
the time interval. The constant speed remains the
9. 380 km
same throughout the time interval
10. 6 min 40 s
11. 2.25 km
14. 65 km/h
12.3
• We can calculate the
instantaneous speed of
an object at a particular
time by calculating the
slope of the tangent to
the line of the distance–
time graph of the
object’s motion.
• Just as we can use
distance and time data
to construct a graph,
we can derive
information about
distance, time, and
speed from a graph.
Calculate:
1. The distance travelled between t=0.5hr and t=1.25 hr
2. The average speed over the first 1.75 hr
3. The speed the car is travelling at at t= 0.25 hr and also t = 2.25 hr
4. In words write a description of the cars movement over the 2.5 hr interval in terms
of speed, time and distance
Answers to Practice Q’s
1. Df – Di = 90km – 50km = 40 km
2.
= Df – Di / tf – ti = (90km - 0 km) / (1.75s – 0s) =
51km/s
3. Calculate the slope of the line at this time since it is constant
there!
At t = 0.25s the speed is: 75km.0.75s = 100
km/s however
at t = 2.25s
(100-90) / (21.75) = 40 km/s
4. The car traveled at a constant speed of 100 km/s
for
the first 0.75 s, then slowed to a constant speed of
for the next 0.25 s before stopping for 0.75 s. In the end
the car was travelling at a constant speed of
40km/s
Answers to 12.3 CYU #1-5
1.
2.
3.
4.
5.
A. The graph shows time from 0-7 s along the horizontal axis and a
distance from 0 to 35 m on the vertical axis B. 4.4 m/s C. 4 m/s D.
The first second E. The third second
The graph would be a straight line slanting upward to the right
A. 42 km/h B. 88 km/h C. Yes the graph of its motion is a straight
line
Draw a tangent to the line of motion at a certain time and calculate
its slope
A. For the first 2 s, the butterfly flies quickly to a point, gradually
slows over the next 2 s, and then stops for 2 s. The butterfly then
flies at a slower but almost constant speed for 4 s. B. 6.8 cm/s C. At
2 s, v = 10 cm/s; at 5.5s, v = 0; at 9s, v = 5cm/s
12.4-Displacement, Time, and Velocity
• Quantities can be either scalar
or vector.
• Scalar quantities only have
magnitude, which is a number
with a unit.
• Vector quantities have both a
magnitude and a direction.
• An object’s speed and velocity can be
described in different ways.
• For example, average speed or velocity,
instantaneous speed, and uniform motion
(constant speed or velocity).
12.4
Displacement and Velocity
• Distance and displacement are similar, but not
identical concepts in science.
VOCABULARY
scalar quantity
displacement
• Distance is a scalar quantity (magnitude only).
vector quantity
• Displacement is a vector quantity (magnitude and
direction)
velocity
• The displacement of an object
is its change in position in
relation to a point of reference.
uniform motion
12.4Displacement,
Time, and Velocity
1
• The motion of an object can be
described by displacement, time, and
velocity.
• Distance and displacement are similar
but not identical concepts in science.
• Speed and velocity are also similar
but not identical concepts.
12.4
Displacement and Velocity
• Speed and velocity are also similar, but not identical concepts.
VOCABULARY
scalar quantity
• Speed is a scalar quantity (magnitude only).
displacement
• Velocity is a vector quantity (magnitude and direction).
vector quantity
velocity
• Velocity is the rate of change of displacement and is given by
the equation:
• The slope of the line of a position–
time graph is equal to the velocity of the
object.
uniform motion
CHAPTER
12
Displacement, Time, and Velocity
• Distance–time graphs and position–time
graphs can visually display information
about an object’s motion.
• The slope of the line is equal to the speed
or velocity of the object.
• If the slope of the line is changing, the
speed or velocity is not constant.
• If the slope the line is constant, the
object is travelling at constant speed or
velocity.
CHAPTER
12
Displacement, Time, and Velocity
Activity
• With a partner, use a mind map to brainstorm different methods of measuring
distance (including length and height of objects).
• For example, you could measure using a ruler, using the length of your arm,
etc.
• Could all of your distance measuring methods be converted to have the same
measurement units, such as metres?
• If you wanted to measure the distance from school to your home, which
method would you use? Explain.
• For more information on distance, read page 341 in the textbook.
CHAPTER
12
Displacement, Time, and Velocity
Key Ideas
• The motion of an object can be described by displacement, time, and
velocity.
• Distance–time graphs and displacement–time graphs can visually display
information about an object’s motion.
• Quantities can be either scalar or vector.
• An object’s speed and velocity can be described in different ways.