topic 1.2 velocity. uniform motion 2 conditions –constant speed –single direction when both the...
TRANSCRIPT
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 …
t
dv
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
Formula?
t
dv
Given this on a formula sheet
?d
Use Algebra
Sample Problem 2[SW] is +ive
Wrong!!!
FYI: Earth’s radius is about 6400km
What we really get is …
????s/h km9000
s)25(h1
km360
d
tvd
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?
?
s25
km/h360
d
t
v
[SW] is +ive
Convert to m/s first
Sample Problem 2[SW] is +ive
Practice1. 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 3Suppose 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.
[N][S]
Initial positionFinal positionkm
Sample Problem 3Suppose 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.
[N][S]
Initial positionFinal positionkm
Sample Problem 3Suppose 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.
[N][S]
Initial positionFinal positionkm
This is displacementkm22d This is the distance travelled
The magnitude of the displacement is the same as the distance travelled when motion is uniform
Sample Problem 3Suppose 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.
[N][S]
Initial positionFinal positionkm
Velocity is displacement over time and is a vector
Sample Problem 3Suppose 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.
[N][S]
Initial positionFinal positionkm
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?
Practice1. 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) Position(m)
0 0
1 +20
2 +40
3 +60
4 +80
Let’s make a position-time graph!
Also called a d-t graph
• Straight-line on a d-t graph means we have uniform motion or constant velocity (and vice versa)
Here’s the Point!!
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 ProblemRunner A
Sample ProblemRunner 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?
m/s0s100
m0
s200s300
m)750(m750
12
12
tt
dd
t
dv
Sample Problem
Find the velocity for section D?
Sample Problem
What was the total distance travelled?
m1500d
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.
t
dv
t
dv avav
calculatest
d
… 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
30 m
start
finish[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
30 m
start
finish[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!!!
AnalogyYears 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
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
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
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
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
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
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
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
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
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 ProblemWhat is the average velocity for the first 5.0s?
Sample ProblemWhat is the average velocity from the 2.0s mark to the 13.0s mark?
Sample ProblemAt what time is the velocity zero?
Somewhere in between 8.0s to 9.5s
Sample ProblemWhat is the instantaneous velocity at 3.0s?
Sample ProblemWhat is the instantaneous velocity at 6.5s?
Sample ProblemWhat is the instantaneous velocity at 11.25s?
The average velocity from 4s to 40s.
The average speed from 4s to 40s.
220m
140m
The time at which the velocity is zero.
Approximately at 26s
The instantaneous velocity at 10s.
The instantaneous velocity at 38s.