Topic 1.2 Velocity. Uniform Motion 2 conditions –Constant speed –Single direction When both the...

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 …

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 …

6702.45 !!!!

Now remember …

Back to the problem …

• What is the velocity of a runner who runs 108m[S] in 12s?

Unit conversion ratio

[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?

Given this on a formula sheet

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

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?

km/h360

[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]

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]

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]

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]

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)

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?

Sample Problem

When, if ever, did the jogger rest?

Sample Problem

State the jogger’s displacement from 0 to 200s?

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

s200s300

m)750(m750

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.

dv avav

calculatest

… 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.

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.

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

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

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

0 21.3

3 36.5

6 43.6

8 47.4

9 49.3

10 51.2

12 55.1

15 63.6

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?

The average velocity from 4s to 40s.

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.

Topic 1.2 Velocity. Uniform Motion 2 conditions –Constant speed –Single direction When both the...

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