Chapter 11 Motion Objectives: Section 1 Use a frame of reference to describe motion Differentiate between Speed and Velocity Calculate the speed of an object Use graphs to describe speed 1
Observing Motion Motion- an object s change in position relative to a reference point. Observe objects in relation to other objects that stay in place. Meter international unit for measuring distance. 1 mm = 50 m Frame of Reference Frame of reference- a system for specifying the precise location of objects in space and time. Object that you assume is fixed in place Normally you think of walls or signs as not moving, or as being stationary objects When you do this you use the walls or signs as a frame of reference? 2
Reference Frame The perception of motion depends on the observer s frame of reference Objects is in motion when object changes position with respect to a frame of reference. Describe the motion observed by one of the boys in the drawing, how does the motion appear to be different to the other boy? 3
Imagine you are the girl observing the bus, describe the motion of each object that you can see Frame of Reference What do you use as your frame of reference most of the time? 4
Displacement Displacement- the change in position of an object. Always includes direction Shorter than distance traveled In the diagram: yellow line = distance black arrow = displacement Measuring Motion: Speed How do you describe motion taking place? To describe motion you discuss speed Speed is the distance an object travels per unit of time 5
Calculating Speed To calculate its speed you divide the distance it travels by the time it travels Speed (S) = distance traveled (d) / the amount of time it took (t). S = d/t Units for speed SI= m/s Depends, but will always be a distance unit / a time unit Ex. Cars: mi./h Jets: km/h Snails: cm/s Falling objects: m/s Calculating speed If I travel 100 kilometer in one hour then I have a speed of 100 km/h S = d/t If I travel 1 meter in 1 second then I have a speed of. 1 m/s 6
Calculating Speed Speed = Distance Time If a runner travels 100 m in 10 seconds what was his average speed? Probably not constant Can solve for the other pieces too Distance = speed x time Time = Distance Speed d Cover the one you re looking for V t Question I travelled 25 km in 10 minutes. How many meters have I travelled? A) 25000 m B).0112 m C).025 m D) 2.5 m 25 km * 1000m/km = 25000 m 7
Practice 1. A car race is 500 km long. It takes the winner 2.5 hours to complete it. How fast was he going? V= 500km 2.5hours V=200 km/hour 2. It is 320 km to Las Vegas. If you average 80 km/hr, how long will it take you to get there? t= 320km 80 km/hr t= 4 hours 3. You are going on a trip. You average 80 km/hr for 6 hours. How far did you go? d= (80km/hr) x 6 hrs d= 480 km Constant speed A moving object that doesn t change it s speed travels at constant speed Constant speed means equal distances are covered in an equal amount of time Suppose you and a friend want to run around a track at constant speed for half an hour 8
Average speed Speed is usually NOT CONSTANT Ex. Cars stop and go regularly Runners go slower uphill than downhill Average speed = total distance traveled total time it took Calculating Average Speed To calculate average speed figure out total distance traveled and divide by total time it took. Problem: It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets. Total Distance: 40 km + 20 km = 60 km Total Time: 1 h + 2 h = 3 hr Ave. Speed: total d/total t = 60 km/3 h = 20 km/h Total _ Dist. Ave. _ Speed = Total _ time 9
Question I ran 1000 m in 3 minutes. Then ran another 1000 m uphill in 7 minutes. What is my average speed? A) 100 m/min B) 2000 m/min C) 10 m/min D) 200 m/min E) 20 m/min Total Dist. = 1000 m + 1000 m = 2000 m Total Time = 3 min + 7 min = 10 min Ave speed = total dist/total time = 2000m/10 min = 200 m/min = D Velocity An objects speed doesn t indicate all there is to know about its motion Velocity the SPEED and DIRECTION of an object. Example: An airplane moving North at 500 mph A missile moving towards you at 200 m/s 10
Measuring Motion: Velocity People often use the word speed when they mean velocity Speed tells how fast an object moves Velocity tells both speed and direction Object always travels in some direction Velocity is a more precise term for describing motion Example: Meteorologists use wind velocity measurements to help predict weather Velocity Is both speed and direction. 40 km/hr = speed 40 km/hr west = velocity Can change velocity two ways Change speed Change directions Young male cheetah covered 100 meters east in 7.19 seconds in a timed run. What is his velocity? 13.9 m/s east 11
How does this graph display speed? Graphing Speed: Distance vs. Time Graphs Denver Phoenix 12
Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/ Rise Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/ Rise=? 600 km 3 h 13
Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/ Rise=? 600 m 3 minutes Rise/ Different Slopes 8 Distance (km) 7 6 5 4 3 2 1 0 Slope = Rise/Run = 1 km/1 hr = 1 km/hr Run = 1 hr Slope = Rise/Run = 0 km/1 hr = 0 km/hr Rise = 1 km Run = 1 hr Rise = 0 km 1 2 3 4 5 6 7 Time (hr) Run = 1 hr Rise = 2 km Slope = Rise/Run = 2 km/1 hr = 2 km/hr 14
Question Average Below Speed is a distance = Total distance/total vs. time graph time of my = 12 km/6 hr position during a race. = 2 km/hr What was my AVERAGE speed for the entire race? Distance (km) 14 12 10 8 6 4 2 0 0 1 2 3 4 5 6 Time (hr) Run = 6 hr Rise = 12 km Why are these graphs different? How was the motion different? 15
Question What does the slope of a distance vs. time graph show you about the motion of an object? It tells you the SPEED Question Below is a distance vs. time graph for 3 runners. Who is the fastest? 7 6 Distance (mi.) 5 4 3 2 1 0 0 1 2 3 4 5 6 35 Time (h) Bob Jane Leroy Leroy is the fastest. He completed the race in 3 hours 16
Section 2 Acceleration Explain changes that occur when objects accelerate Graph acceleration Acceleration Any change in velocity is acceleration, even if the speed of the object remains the same. When ever an object changes how it moves, the velocity changes. A change in direction is a change in velocity, and acceleration. 17
Acceleration Acceleration the rate at which velocity changes Can be an: Increase in speed Decrease in speed Change in direction Types of acceleration Increasing speed Example: Car speeds up at green light Decreasing speed Example: Car slows down at stop light screeeeech Changing Direction Example: Car takes turn (can be at constant speed) 18
Question How can a car be accelerating if its speed is a constant 65 km/h? If it is changing directions it is accelerating Calculating Acceleration If an object is moving in a straight line Units of acceleration: m/s 2 Acceleration = V a t Final _ speed Initial _ Speed Time a = (V f )-(V i ) Time a= v t 19
Calculating Acceleration a= v t To calculate acceleration, substrate the difference between final speed and initial speed. Then divide by time Acceleration= Final Speed(V f ) Initial Speed (V i ) Time a= 16 m/s 0 m/s 4s a= 16 m/s 4s a= 4 m/s 2 0 s 1 s 2 s 3 s 4 s 0 m/s 4 m/s 8 m/s 12 m/s 16 m/s Initial Speed Final Speed Question A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver s average acceleration? Accel= Final Speed Initial Speed Time = 40m/s 20 m/s 2s =20 m/s 2s = 10m/s 2 20
Acceleration Practice Problems 1. Natalie accelerates her skateboard along a straight path from o m/s to 4.0 m/s in 2.5 s. Find her average acceleration. Final speed (V f )= 4.0 m/s Initial speed (V i ) = 0 m/s Time=2.5s a =? a= 4.0 m/s 0 m/s 2.5 s a= 1.6 m/s 2 2. A turtle swimming in a straight line toward shore has a speed of 0.50 m/s. After 4.0s, its speed is 0.80 m/s. What is the turtle s average acceleration? V f = 0.80 m/s V i = 0.50 m/s Time= 4.0 s a =? a= 0.80 m/s 0.50 m/s 4.0 s a= 0.075 m/s 2 3. Mai s car accelerates at an average rate of 2.6 m/s 2. How long will it take her car to speed up from 24.6 m/s to 26.8 m/s? V f = 26.8 m/s V i = 24.6 m/s Time=? a= 2.6 m/s 2 t= V a t= 26.8 m/s 24.6 m/s 2.6 m/s 2 t= 0.85 s Acceleration Practice Problems 4. Tom is driving down I-75. He notices a police officer and slows down from 81 m/s to 62 m/s in 5.0 s. Calculate his acceleration. V f = 62 m/s V i = 81 m/s Time= 5.0 s a=? a= 62 m/s 81 m/s 5.0 s a= -19 m/s 5.0 s a= -3.8 m/s 2 5. A cyclist travels at a constant velocity of 4.5 m/s westward and then speeds up with a steady acceleration of 2.3 m/s 2. Calculate the cyclist s speed after accelerating for 5.0s. V f = V i + at V f = 4.5 m/s + (2.3 m/s 2 x 5.0 s) V f = 16 m/s 21
Graphing Acceleration Can use 2 kinds of graphs Speed vs. time Distance vs. time Graphing Acceleration: Speed vs. Time Graphs 14 12 Speed (m/s) 10 8 6 4 2 0 0 1 2 3 4 5 6 Time (s) 1) Speed is increasing with time = accelerating 2) Line is straight = acceleration is constant 22
Graphing Acceleration: Speed vs. Time Graphs 14 12 Speed (m/s) 10 8 6 4 2 0 Rise = 4 m/s Run = 2 s 0 1 2 3 4 5 6 Time (s) 1) In Speed vs. Time graphs: Acceleration = Rise/Run Find the acceleration = 4 m/s 2 s = 2 m/s 2 Graphing Acceleration: Distance vs. Time Graphs 35 30 Distance (m) 25 20 15 10 5 0 0 1 2 3 4 5 Time (s) 1) On Distance vs. Time graphs a curved line means the object is accelerating. 2) Curved line also means your speed is increasing. Remember slope = speed. 23
Question 14 12 Speed (m/s) 10 8 6 4 Run = 3 s Rise = -6 m/s 2 0 0 1 2 3 4 5 6 Time (s) Above is a graph showing the speed of a car over time. 1) How is the speed of the car changing (speeding up, Slowing down, or staying the same)? 2) What is this car s acceleration? 1) The car is slowing down 2) Acceleration = rise/run = -6m/s 3s = -2 m/s 2 Question: Distance (m) 35 30 25 20 15 10 5 0 0 1 2 3 4 5 Time (s) The black and red lines represent a objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so must be slowing down 1) Which Remember: line represents in distance vs. object time graphs: that is accelerating? curved line = accelerating, flat line = constant speed 24
Question: Hard one Distance (m) Speed (m/s) 14 45 12 40 10 35 8 30 6 25 420 215 010 5 0 0 1 2 3 4 5 6 Time (s) 0 1 2 3 4 5 6 Time (s) Above is a graph showing the speed of a car over time. 1)What would a distance vs. time graph for this look like? Understanding the formula o Acceleration= final velocity- starting velocity time o Change in velocity = final starting velocity velocity o Acceleration= change in velocity time a= v t 25
Positive acceleration Negative acceleration Motion in a circle An object moving in a circle or a curve is constantly changing direction. Centripetal = acceleration towards the center of the circle. 26