Physics Notes Part III. Uniform/Non-uniform Motion and Graphing
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1 Physics Notes Part III Uniform/Non-uniform Motion and Graphing
2 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).
3 Ticker Tape a device that uses a sequence of dots to track motion of object for uniform motion for uniform motion for uniform motion
4 Uniform motion on a distance time (d-t) graph moves at the same rate graphed as a straight line Example: d t Uniform motion on a velocity time graph (v-t) moves at the same speed graphed as a horizontal line. Example: v t
5 Sometimes describing motion is hard to do with words. Graphs make it easier to picture. 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
6 Distance-Time Graphs On your paper, graph the following: (Y) d (m) (X) t (s) Ordered Pair (X,Y) format
7 Distance Time Graph Distance (m) Time (s)
8 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.
9 Slope = AKA Speed Which is moving the fastest? The slowest?
10 On a distance time graph for uniform motion the slope equals the average speed. V avg d t
11 Example: What is the V avg for this graph? Page 465 #3-6
12 Displacement -Time Graphs 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
13 If slope is positive, the object is moving at a constant speed to the right, north, or east.
14 If slope is negative, the object is moving at a constant speed to the left, south, or west.
15 If slope is zero, object is stopped (at rest).
16 Describe the motion of each graph:
17 To calculate the change in displacement from a graph:
18 Example: Use this graph to answer the questions on the following slide.
19 a) What is the object s initial position (d 1 )? b) What is the object s final position (d 2 )? 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 1s b) 1s 3s c) 3s 4.5s d) 4.5s 6s f) Describe the motion of the object for the 6 s trip.
20 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 10s b) 10s 15s c) 15s 40s d) 40s 55s c) Describe the motion of the object for the 55 s trip. P. 450 # 1,2,4
21 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?
22 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. Y D (m) T (min) X A) What are the points on the graph?
23 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
24 Graphs for objects slowing down:
25 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.
26 Page 442 #8a
27 d Tangent Lines t On a position vs. time graph: The slope of a tangent line will give the velocity at that point in time. ( instantaneous velocity ) SLOPE Positive Negative Zero VELOCITY Positive Negative Zero
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32 Over the next few slides we will summarize some facts about graphs and motion. Velocity-time Graphs: The basics
33 A horizontal line means constant velocity... (ie: acceleration is zero) in a positive direction in a negative direction
34 Accelerating to the right. Accelerating to the left.
35 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.
36 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.
37 Describe the motion depicted by the v-t graph below
38 Describe the motion depicted by the v-t graph below
39 Describe the motion depicted by the v-t graph below
40 Describe the motion depicted by the v-t graph below
41 The slope of a velocity-time graph is the average acceleration. *The units for acceleration are always squared* Example: m/s 2
42 Example: Calculate the average acceleration.
43 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.
44 Example: Calculate the displacement from the velocity-time graph.
45 Example: Calculate the displacement from the velocity-time graph.
46 Worksheet on v-t graphs V-t graph Assignment
47 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
48 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.
49 To calculate acceleration: To calculate average acceleration: a v v v 2 1 t t2-t 1 a v1 = acceleration = initial velocity v 2 t = final velocity = change in time
50 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?
51 Example 2: A rabbit, eating in a field, scents a fox nearby and races off. It takes only 1.8 s to reach a top velocity of 7.5 m/s [N]. What is the rabbit s acceleration during this time?
52 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/s 2 for 7.0s, what is your final speed?
53 Example 4: A skidoo travelling at a constant speed approaches the top of a hill. The skidoo rolls down the hill at 4.0m/s 2 for 16.0s and reaches a final speed of 52m/s. What was the initial speed of the skidoo before rolling down the hill?
54 Example 5: You re a drag racer. Your acceleration is 26.6 m/s 2, and your final speed is m/s. How long did it take to reach your final speed?
55 Non-constant positive acceleration (speeding up) In a positive direction In a negative direction
56 Non-constant negative acceleration (slowing down) In a positive direction In a negative direction
57 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.
58 Identify the parts of the bicycle, talk about the functions of these parts and explain how a bicycle generates motion.
59 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. 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
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Comment: Unlike distance, displacement takes into consideration the direction of motion from the point of origin (where the object starts to move).
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