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• Speed ( ) is the distance
an object travels divided
by the time to travel that
distance.
• In other words
– Speed is a scalar
quantity (no direction).
These two ski gondolas
have the same speed but
have different velocities
since they are travelling
in opposite directions.
• Velocity ( ) is the displacement of an
object divided by the time interval.
• In other words
• Velocity describes how fast an object’s
position is changing.
•Velocity is a vector quantity (direction).
•The units for velocity and speed are metres
per second (m/s).
Calculating the Slope of the
Position-Time Graph
• To learn more about velocity, we must now
understand straight line graphs.
• The slope of a graph is represented by
Finding the Slope of a Line
1. Pick two points
on the grid.
2. Make a triangle
3.
500
400
Position (m)
Ch. 8.2 Average Velocity
300
400
200
100
– rise = change in y-axis
– run = change in x-axis
4. Units = metres/second
So slope = 36.4 m/s
11
0
14
2
16
4
18
6
8
10
12
20
Time(s)
1
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Position – Time Graph
• On a position-time graph the slope is
the change in position (
) divided by
the change in time (
).
Example
Which jogger’s
motion has a
greater slope?
Which jogger is
moving faster?
What is the slope
of each line?
What is each
jogger’s
?
Average Velocity
• Usually, objects do not move at a perfectly
constant speed.
• For this reason, we often use “average velocity” in
our calculations.
• The slope of a position-time graph is the object’s
average velocity ( ).
• Average velocity is the rate of change in position
for a time interval.
• Remember ,
(average velocity), is a
vector and we must therefore always
include a direction.
• If we were to discuss
, (average
speed), we do not need to include
direction, because speed is a scalar.
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Calculating Average Velocity
On a position-time graph if “forward” is
given a positive direction:
• A positive slope means that the object’s
average velocity is forward.
The relationship between average velocity,
displacement, and time is given by:
• A negative slope means that the object’s
average velocity is backwards.
1. What is the average velocity of a dog that takes
4.0 s to run forward 14 m?
Example 1
• Zero slope means the object’s average
velocity is zero.
Example 2
1. A boat travels 280 m East in a time of 120 s. What
is the boat’s average velocity?
Calculating Displacement
The formula for finding velocity can be
rearranged so that you can solve for
either displacement or time.
You can solve for displacement by taking this
equation and multiplying both sides by ∆t leaving
the equation:
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31
Example 3
1. What is the displacement of a bicycle that travels
8.0 m/s [N] for 15 s?
Calculating Time
Use the last equation to solve the following:
Example 4
Solve this problem on your own,
using the same steps.
4.A person, originally at the starting
line, runs west at 6.5 m/s. What
is the runner’s displacement after
12 s?
Answer: 78 m West
Converting between m/s and km/h
• To convert from km/h to m/s
– Change km to m: 1 km = 1000 m
– Change h to s: 1 h = 3600 s
1. How long would it take a cat walking north at 0.80
m/s to travel 12 m north?
• Therefore multiply by 1000 and
divide by 3600
or
Solution:
2. A car is driving forward at 15 m/s. How long would it
take this car to pass through an intersection that is
• Divide the speed in km/h by 3.6 to
obtain the speed in m/s.
For example, convert 75 km/h to m/s.
11 m long?
Solution:
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31
Converting between m/s and km/h
Try the following unit conversion problems yourself.
1. Convert 95 km/h to m/s.
• 95 km X 1000m X 1hr
= 26 m/s
1hr
1km
3600s
2. A truck’s displacement is 45 km north after driving for 1.3
hours. What was the truck’s average velocity in km/h &
m/s?
Vav = 45km
1.3hr
= 35 km/h N or
9.6 m/s N
3. What is the displacement of an airplane flying
480 km/h [E] during a 5.0 min time interval?
d = 480 km X .083 hr 40 km [E] or
hr
000 m [E]
Take the Section40,
8.2 Quiz
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