Topic 1.2 Velocity
Uniform Motion
• 2 conditions
– Constant speed
– Single direction
• When both the speed and direction remain
the same, we say the velocity is constant
or uniform
Mathematically defined as …

 d
v
t
Velocity is a vector
displacement
time
interval is
a scalar
Sample Problem 1
• What is the velocity of a runner who runs 108m[S]
in 12s?
[S] is +ive
What is it in km/h?
• Is …
1=3?
• Is …
1 yd = 3 ft ?
• What about …
1 km = 1000 m ?
• What if we divide both sides by 1000 m?
What is …
6702.45 …
multiplied by …
1
6702.45 !!!!
Now remember …
Back to the problem …
• What is the velocity of a runner who runs
108m[S] in 12s?
Unit conversion ratio
Back to the problem …
• What is the velocity of a runner who runs
108m[S] in 12s?
Back to the problem …
• What is the velocity of a runner who runs
108m[S] in 12s?
[S] is +ive
Or …
• How many seconds are in an hour?
Now recall our original answer
• How many numbers do you see?
• There are actually 2!!!
• Velocity is a ratio of 2 numbers
Sample Problem 2
• An air traffic controller notices that a distant
aircraft has a velocity of 360 km/h [SW]. What
displacement will the plane experience in the 25
s period before the controller checks its position
again?
[SW] is +ive

 d
v
t
Formula?

d  ?
Given this
on a formula
sheet
Use Algebra
Sample Problem 2
[SW] is +ive
FYI: Earth’s
radius is
about
6400km
Wrong!!!
What we really get is …
 
  360km 
d  v  t  
(25s)
 1h


d  9000km  s/h ????
Sample Problem 2
• An air traffic controller notices that a distant
aircraft has a velocity of 360 km/h [SW]. What
displacement will the plane experience in the 25
s period before the controller checks its position
again?
[SW] is +ive

v  360 km/h
t  25s

d  ?
Convert to
m/s first
Sample Problem 2
[SW] is +ive
Practice
1. What is the velocity of an airplane that
experiences a displacement of 580 m[N] in 2.5s?
2. A car has a velocity of 29 m/s[E]. What is its
displacement if it travels at this velocity for 2
hours?
3. How long would it take for a dolphin swimming at
8.0 m/s[W] to travel 208 m[W]?
4. What velocity is required for a truck moving
along the highway to experience a displacement
of 400 m [S] in a time of 20 s? Express your
answer in both metres per second and
kilometres per hour.
Assignment 1 on Topic 1.2
• Due Friday at the beginning of class
Sample Problem 3
Suppose a car travels with uniform motion from a
position of 2.0 km[N] to a position of 20 km[S] in
0.50 h. Find the car’s displacement.
[S]
[N]
km
Final position
Initial position
Sample Problem 3
Suppose a car travels with uniform motion from a
position of 2.0 km[N] to a position of 20 km[S] in
0.50 h. Find the car’s velocity.
[S]
[N]
km
Final position
Initial position
Sample Problem 3
Suppose a car travels with uniform motion from a
position of 2.0 km[N] to a position of 20 km[S] in
0.50 h. Find the car’s distance travelled.
[S]
[N]
km
Final position
Initial position
This is displacement
d  22 km
This is the distance travelled
The magnitude of the displacement is the same
as the distance travelled when motion is uniform
Sample Problem 3
Suppose a car travels with uniform motion from a
position of 2.0 km[N] to a position of 20 km[S] in
0.50 h. Find the car’s speed.
[S]
Final position
[N]
km
Initial position
Velocity is displacement
over time and is a vector
Sample Problem 3
Suppose a car travels with uniform motion from a
position of 2.0 km[N] to a position of 20 km[S] in
0.50 h. Find the car’s speed.
[S]
Final position
[N]
km
Initial position
Speed is distance over time and is a scalar
Sample Problem 4
• How long does it take for a car traveling at 60
km/h to travel a distance of 20 m?
Practice
1. The tip of a tuning fork moves 1.1 mm in
4.0×10-3s. What is its speed in metres per
second? (Note 1m =1000mm)
2. How long does the goalkeeper for a hockey
team have to react if a puck travelling at
25m/s is unexpectedly deflected and
changes direction without slowing down
when it is at a distance of 10m away.
3. How far does a car with it’s cruise control
set to 110km/h travel in 10 minutes?
Graphing Motion
+20 m/s
Time (s)
0
1
2
3
4
Position(m)
0
+20
+40
+60
+80
Let’s make a position-time graph!
Also called a d-t graph
Here’s the Point!!
• Straight-line on a d-t graph means we
have uniform motion or constant
velocity (and vice versa)
Can we determine an object’s
velocity from its d-t graph?
Wait a minute …
This is the
slope formula!!!
Big idea!!
• The velocity is equal to the slope of the
line on a d-t graph
Sample Problem
Runner A
Sample Problem
Runner C
Practice
• See handout
Sample Problem
When was the jogger running the fastest?
A
Sample Problem
When, if ever, did the jogger rest?
C
Sample Problem
State the jogger’s displacement from 0 to 200s?
+750m
Sample Problem
State the jogger’s displacement from 100 to 300s?
+250m
Sample Problem
State the jogger’s displacement from 300 to 500s?
-750m
Sample Problem
State the jogger’s displacement from 0 to 500s?
0m
Sample Problem
Find the velocity for section A?
Sample Problem
Find the velocity for section B?
Sample Problem
Find the velocity for section C?
  
 d d 2  d1  750m  (750m) 0m
v



 0m/s
t
t2  t1
300s  200s
100s
Sample Problem
Find the velocity for section D?
Sample Problem
What was the total distance travelled?
d  1500 m
Practice
Assignment
The above position-time graph could
not actually represent the motion of a
real object. Why?
This one could.
When velocity changes …
… we calculate the average velocity and the
average speed.

d

vav 
t
d
vav 
t

d
t
calculates
… the exact velocity when motion is
uniform
… the average velocity when it isn’t
Sample problem
• A football player warming up for a game jogs along the
sideline. He jogs 50 m[N] and then jogs 30 m[S] back
toward his starting point before stopping to talk to his coach.
If he jogged for 20 s, determine his average velocity.
50 m
start
finish
30 m
[N] is +ive
Sample problem
• A football player warming up for a game jogs along the
sideline. He jogs 50 m[N] and then jogs 30 m[S] back
toward his starting point before stopping to talk to his coach.
If he jogged for 20 s, determine his average speed.
50 m
start
finish
30 m
[N] is +ive
Sample Problem
• For the time interval from 4.0 s to 20 s
determine the average velocity
The average velocity is equal to the slope of the
straight line joining the two points on a d-t graph
Sample Problem
• For the time interval from 4.0 s to 20 s
determine the average speed
Practice
Assignment
• Let me tell you why you're here. You're
here because you know something.
What you know you can't explain, but
you feel it. You've felt it your entire life,
that there's something wrong with the
world. You don't know what it is, but it's
there, like a splinter in your mind,
driving you mad. It is this feeling that
has brought you to me. Do you know
what I'm talking about?
Instantaneous Velocity
• This is your last chance. After
this, there is no turning back. You
take the blue pill - the story ends,
you wake up in your bed and
believe whatever you want to
believe. You take the red pill - you
stay in Wonderland and I show
you how deep the rabbit-hole
goes.
You are all laboratory babies!!!
Analogy
Years since birth Height (inches)
0
21.3
3
36.5
6
43.6
8
47.4
9
49.3
10
51.2
12
55.1
15
63.6
18
66
Average = 43.5
Average = 50.0
Average = 49.4
Average = 49.3
What was the height on its 9th birthday?
Sample Problem
What is the average velocity for the
first 5.0s?
Sample Problem
What is the average velocity from
the 2.0s mark to the 13.0s mark?
Sample Problem
At what time is the velocity zero?
Somewhere in between
8.0s to 9.5s
Sample Problem
What is the instantaneous velocity
at 3.0s?
Sample Problem
What is the instantaneous velocity
at 6.5s?
Sample Problem
What is the instantaneous velocity
at 11.25s?
The average velocity from 4s to 40s.
140m
220m
The average speed from 4s to 40s.
The time at which the velocity is zero.
Approximately at 26s
The instantaneous velocity at 10s.
The instantaneous velocity at 38s.