Physics Notes Part III Uniform/Non-uniform Motion and …...•Like distance time graphs, but with direction (can be either positive or negative). •The y-intercept is the initial

Physics Notes – Part III

Uniform/Non-uniform Motion and Graphing

Uniform Motion

Rolling ball is an example of uniform motion.

1) Speed of the ball is constant (with no friction).

2) In a straight line (direction unchanging).

Ticker Tape – a device that uses a sequence of dots to track motion of object

for uniform motionfor uniform motion for uniform motion

Uniform motion on a distance time (d-t) graph moves at the same rate – graphed as a straight line

Uniform motion on a velocity time graph (v-t) moves at the same speed – graphed as a horizontal line.

d

t

t

v

Example:

Example:

P. 227 # 1-3 and 5-9

Expectations for Graphing• Pencil • Ruler • Title (centered and underlined)• Arrows and label axis (x, y)• Time is always the independent variable (x)• Use squiggle for a big jump in the numbers• If the points are not in a linear path, draw a line of best fit.• If on same axis – skip count numbers same and skip same

amount of blocks between each number• ¾ page

Sometimes describing motion is hard to do with words. Graphs make it easier to picture.

Distance-Time Graphs

On your paper, graph the following:

d (m) t (s)

0 0

5 7

10 14

15 21

(X)(Y) Ordered Pair – (X,Y) format

Distance – Time Graph

Distance(m)

Time (s)

•A d-t graph which is a straight line indicates constant speed.

•The object is not speeding up or slowing down.

(The acceleration is zero.)

•The steeper the line, the faster the object is going.

Which is moving the fastest? The slowest?

Slope =AKASpeed

On a distance time graph for uniform motion the slope equals the average speed.

avg

dV

t

= =

Example: What is the Vavg for this graph?

What is the Vavg for this graph?

P. 223 Activity 5-3B/Assignment #1

Graphing wkst #1&2 Graphing Motion wkst

•Aka: position-time graphs

• Like distance time graphs, but with direction (can be either positive or negative).

• The y-intercept is the initial position (right/left, Up/Down, N/S, E/W).

• Slope = velocity

Displacement -Time Graphs

If slope is positive, the object is moving at a constant speed to the right, north, or east.

If slope is negative, the object is moving at a constant speed to the left, south, or west.

If slope is zero, object is stopped (at rest).

Describe the motion of each graph:

Answers on next page – please sketch all 4 now and place answers underneath each graph)

Answers:

To calculate the change in displacement from a graph:

This was the formula that is on the periodic table!!!

Example: Use this graph to answer the questions on the following slide.

Don’t forget to add a decimal zero when extracting numbers from a graph!!

Find total distance

a) What is the object’s initial position (d1)?b) What is the object’s final position (d2)?c) What was the object’s displacement for the 6s trip?d) What was the total distance the object travelled?e) What is the velocity of the object during these time

intervals:a) 0s – 1sb) 1s – 3sc) 3s – 4.5sd) 4.5s – 6s

f) Describe the motion of the object for the 6 s trip.

New formula for displacement –on a graph! –this one is on the periodic table

Answers!!!

Example: Use this graph to answer the questions.

a) What was the total distance the object travelled?

b) What is the velocity of the object during these time intervals:

a) 0s – 10sb) 10s – 15sc) 15s – 40sd) 40s – 55s

c) Describe the motion of the object for the 55 s trip. P. 450 # 1,2,4

ANSWERS!!!

a) What was the total distance the object travelled?

b) What is the velocity of the object during these time intervals:

a) 0s – 10sb) 10s – 15sc) 15s – 40sd) 40s – 55s

c) Describe the motion of the object for the 55 s trip. P. 450 # 1,2,4

A. Describe what is happening in each leg of the trip.

B. During which parts of the trip is the object stopped?

C. During which part of the trip is the object moving the fastest? What is its Velocity?

A. Describe what is happening in each leg of the trip.

B. During which parts of the trip is the object stopped?

C. During which part of the trip is the object moving the fastest? What is its Velocity?

ANSWERS!!!

P. 223 Activity 5-3B

Graphing worksheet – tell a story

Construct a displacement-time graph.

A fox started its hunting trip from her den (point A). She walked 15m[N] for 10 minutes. She smelled a rabbit and stood still for 2 minutes. She ran 25m[S] for 3 minutes after the rabbit. Rabbit went down hole and she stood watching the hole for 4 minutes. Conceding defeat, she returned to her den, 25 minute trip.

A) What are the points on the graph?

Y

X

D (m) T (min)

Y

X

D (m) T (min)

Construct a displacement-time graph for the following situation:

A fox started its hunting trip from her den (point A). She walked 15m[N] for 10 minutes. She smelled a rabbit and stood still for 2 minutes. She ran 25m[S] for 3 minutes after the rabbit. Rabbit went down hole and she stood watching the hole for 4 minutes. Conceding defeat, she returned to her den, a total 25 minute trip.

Displacement graph worksheet

Displacement-Time Graphs for Non-Uniform Motion

When an object is accelerating, the d-t graph will be curved.

Graphs for objects speeding up:

-North-East-right-up

-South-West-left-down

Graphs for objects slowing down:

To find instantaneous velocity on a curved d-t graph:

1. Draw a tangent line that touches the curve at one point using a RULER.

2. Find 2 points on the tangent.

3. Calculate the slope.

The slope of the tangent line is the instantaneous velocity.

Tangent Lines

t

SLOPE VELOCITY

Positive Positive

Negative Negative

Zero Zero

d

On a position vs. time graph:

The slope of a tangent line will give the velocity at that point in time. ( instantaneous velocity )

• Over the next few slides we will summarize some facts about graphs and motion.

•Velocity-time Graphs: The basics

A horizontal line means constant velocity...

(ie: acceleration is zero)

in a positive direction in a negative direction

Accelerating to the right.

Accelerating to the left.

Starts with an initial speed to the right but slows down and stops.

Starts with an initial speed to the left but slows down and stops.

Describe the motion depicted by the v-t graph below:

The object starts with an initial speed to the left and accelerates to the right.

Describe the motion depicted by the v-t graph below

Answer At time zero the object is already moving to the right. It continues to accelerate to the right.

At time zero, there is already a positive value for the speed. As time goes on, the positive speeds increase. That is, the object picks up speed to the right.

Answer

Answer

AnswerThe object is moving to the

right but decelerating. It therefore slows down and stops.

At time zero, there is already a positive value for the speed. As time goes on, the positive speeds decrease. The object keeps moving to the right but slows down and stops.

Explanation

Answer The object starts with an initial speed to the left but slows down and stops.

At time zero, the object has a maximum speed to the left . However, as time increases, speed decreases, and the object stops.

Explanation

Answer The object starts with an initial speed to the left and accelerates to the right.

At time zero, the object has a maximum speed to the left . However, as time increases, speed decreases, and the object stops. But it continues to accelerate to the right, meaning that after its brief stop, it took off to the right.

Gravity

Path of a ball when thrown up and caught

The slope of a velocity-time graph is the average acceleration.

*The units for acceleration are always squared*

Example: m/s2

Example: Calculate the average acceleration.

22 1

2 1

8 4 42 /

4 2 2

y ya Slope m s

x x

− −= = = = =

− −

Answers

On a velocity - time graph the area between the graphed line and the x-axis equals the displacement.

Example: Calculate the displacement from the velocity-time graph.

On a velocity - time graph the area between thegraphed line and the x-axis equals the displacement

Area = l x w = 6 s x 30 m/s = 180 m

To find out theDistance travelledOn a v-t graph!!

Example: Calculate the displacement from the velocity-time graph.

Object is moving at a constant speed for 5.0 sthen it speeds up for the next 5.0 sec.

Re tan

2

(10.0 / )(5.0 )(10.0 )(5.0 / )

2

50 25

75

c gle Triangled A A

bhlw

m s ss m s

m m

m

= +

= +

= +

= +

=

Displacement is equal to the area between the drawn line and the x-axis

Example:Calculate the displacement from the velocity-time graph.

Worksheet on v-t graphs

V-t graph Assignment

ACCELERATION

• Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity

CONSTANT ACCELERATION• Sometimes an accelerating object will change its velocity by

the same amount each second. This is known as a constant acceleration since the velocity is changing by the same amount each second.

Acceleration

• https://www.youtube.com/watch?v=e5Gl2LLLAGo

• Acceleration explained

https://www.youtube.com/watch?v=e5Gl2LLLAGo

To calculate acceleration:

= acceleration= initial velocity

2 1v vvat t

−= =

a 2v

1v t= final velocity = change in time

To calculate averageacceleration:

2-t1

Solve for t

2 1v vvat t

−= =

Solve for Initial velocity

2 1v vvat t

−= =

Solve for Initial Velocity

2 1v vvat t

−= =

Example 1:

A skier is moving at 1.8 m/s (down) near the top of a hill. 4.2 s later she is travelling at 8.3 m/s (down). What is her acceleration?

Example 2:

A rabbit, eating in a field, scents a fox nearby and races off. The rabbit reaches a top velocity of 7.5 m/s [N]. If the rabbit accelerates as 4.4 m/s2 , How long will it take the rabbit to reach its hole?

Example 2: A rabbit, eating in a field, scents a fox nearby and races off. The rabbit reaches a top velocity of 7.5 m/s [N]. If the rabbit accelerates as 4.4 m/s2 , How long will it take the rabbit to reach its hole?

Example 3:

You are coasting on your skateboard at 1.4 m/s [N]and you decide to speed up. If you accelerate at 0.50m/s2 for 7.0s, what is your final velocity?

Example 4:

A skidoo travelling at a constant speed approaches the top of a hill. The skidoo rolls down the hill at 4.0m/s2 for 16.0s and reaches a final speed of 52m/s. What was the initial speed of the skidoo before rolling down the hill?

Example 5:

You’re a drag racer. Your acceleration is 26.6 m/s2, and your final velocity is 146.3 m/s. How long did it take to reach your initial velocity?

Acceleration work problem worksheet

Non-constant positive acceleration (speeding up)

In a positive direction In a negative direction

Non-constant negative acceleration (slowing down)

In a positive direction In a negative direction

Describe the motion depicted on this v-t graph.

The object is initially at rest, speeds up in a negative direction to a constant speed, then slows down to a stop, still travelling in the same direction.

Identify the parts of the bicycle, talk about the functions of these parts and explain how a bicycle generates motion.

1. Uno Motorcycle

2. Confederation Bridge

3. Elsie MacGill

4. Wallace Turnbull

5. Bombardier

6. Canadian Space Agency

7. Canadarm

8. Bluenose

9. National Railway

10. Silver Dart

11. Bushplanes

Research Activity - Canadian Contributions to Motion Technologies

You will be assigned one of the following topics. Describe the contribution made to motion-related science and technology and present your findings to the class.

Acceleration Lab

https://www.youtube.com/watch?v=-xjHLFTQvjo – ticker tape apparatus

Midpoint time=

Time interval =

Change in distance = measure from middle of point to the middle of next point – be as accurate as possible – nearest hundredths

Total distance =

Speed =

https://www.youtube.com/watch?v=5KtxGdRihLk – analysing ticker tape

https://www.youtube.com/watch?v=-xjHLFTQvjohttps://www.youtube.com/watch?v=5KtxGdRihLk

Documents

Physics Notes Part III Uniform/Non-uniform Motion and …...•Like distance time graphs, but with direction (can be either positive or negative). •The y-intercept is the initial