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## MOTION

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**Chapter Four: Motion**• 4.1 Position, Speed and Velocity • 4.2 Graphs of Motion • 4.3 Acceleration**Section 4.1 Learning Goals**• Explain the meaning of motion. • Describe an object’s position relative to a reference point. • Use the speed formula. • Tell the difference between speed and velocity.**Position is a variable given relative to an origin.**• The origin is the place where position equals 0. • The position of this car at 50 cm describes where the car is relative to the track. 4.1 Position, Speed and Velocity**Position and distance are similar but not the same.**If the car moves a distance of 20 cm to the right, its new position will be 70 cm from its origin. 4.1 Position, Speed and Velocity Distance = 20 cm New position**The variable speeddescribes how quickly something moves.**To calculate the speed of a moving object divide the distance it moves by the time it takes to move. 4.1 Position, Speed and Velocity**The units for speed are distance units over time units.**This table shows different units commonly used for speed. 4.1 Position, Speed and Velocity**When you divide the total distance of a trip by the time**taken you get the average speed. Total distance /Total time On this driving trip around Chicago, the car traveled and average of 100 km/h. 4.1 Average speed**A speedometer shows a car’s instantaneous speed.**The instantaneous speed is the actual speed an object has at any moment.(At that instance) 4.1 Instantaneous speed**Solving Problems**How far do you go if you drive for two hours at a speed of 100 km/h? • Looking for: • …distance • Given: • …speed = 100 km/h time = 2 h • Relationships: • d = vt • Solution: • d = 100 km/h x 2 h = 200 km = 200 km**4.1 Vectors and velocity**• Position uses positive and negative numbers. • Positive numbers are for positions to the right of the origin and negative numbers are for positions to the left the origin.**4.1 Vectors and velocity**• Distance is either zero or a positive value.**4.1 Vectors and velocity**• We use the term velocity to mean speed with direction. • (Speed +Direction= Velocity) Video**4.1 Keeping track of where you are 1**• Pathfinder is a small robot sent to explore Mars. • It landed on Mars in 1997. • Where is Pathfinder now?**4.1 Keeping track of where you are 2**• Pathfinder keeps track of its velocity vector and uses a clock. • Suppose Pathfinder moves forward at 0.2 m/s for 10 seconds. What is Pathfinder’s velocity?**4.1 Keeping track of where you are 3**• Suppose Pathfinder goes backward at 0.2 m/s for 4 seconds. What is Pathfinder’s change in position?**4.1 Keeping track of where you are 4**• The change in position is the velocity multiplied by the time.**4.1 Keeping track of where you are 5**• Each change in position is added up using positive and negative numbers. • Pathfinder has a computer to do this.**4.1 Maps and coordinates**• Out on the surface of Mars, Pathfinder has more choices. • The possible directions include north, east, south, and west, and anything in between. • If Pathfinder was crawling on a straight board, it would have only two choices for direction.**4.1 Maps and coordinates**• This kind of graph is called a map. • Street maps often use letters and numbers for coordinates. • A graph using north−south and east−west axes can accurately show where Pathfinder is.**4.1 Vectors on a map 1**• Suppose you run east for 10 seconds at a speed of 2 m/s. • Then you turn and run south at the same speed for 10 more seconds. • Where are you compared to where you started? • Vector Rap**4.1 Vectors on a map 2**• To get the answer, you figure out your east−west changes and your north−south changes separately. origin = (0 , 0)**4.1 Vectors on a map 3**• Your first movement has a velocity vector of +2 m/s, west-east (x-axis). • After 10 seconds your change in position is +20 meters (east on x-axis). Distance is velocity x time (d = v x t) d = 2 m/s x 10 s = +20 m**4.1 Vectors on a map 4**• Your second movement has a velocity vector of −2 m/s north−south (y-axis) • In 10 seconds you move −20 meters (south is negative on y-axis) New position = (+20 , -20) d = 2 m/s x 10 s = -20 m**Solving Problems**A train travels at 100 km/h heading east to reach a town in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now? • Looking for: • …train’s new position • Given: • …velocity = +100 km/h, east ; time = 4 h • …velocity = -50 km/h, west ; time = 4 h • Relationships: • change in position = velocity × time**Solving Problems**• Solution: • 1st change in position: • (+100 km/h) × (4 h) = +400 km • 2nd change in position: • (−50 km/h) × (4 h) = −200 km • Final position: • (+400 km) + (−200 km) = +200 km • The train is 200 km east of where it started.**Chapter Four: Motion**• 4.1 Position, Speed and Velocity • 4.2 Graphs of Motion • 4.3 Acceleration**Section 4.2 Learning Goals**• Construct and analyze graphs of position versus time, and speed versus time. • Recognize and explain how the slope of a line describes the motion of an object. • Explain the meaning of constant speed.**4.2 Graphs of Motion**• Constant speed means the speed stays the same. • An object moving at a constant speed always creates a position vs. time graph that is a straight line.**4.2 Graphs of Motion**• The data shows the runner took 10 seconds to run each 50-meter segment. • Because the time was the same for each segment, you know the speed was the same for each segment.**4.2 Graphs of Motion**• You can use position vs. time graphs to compare the motion of different objects. • The steeper line on a position vs. time graph means a faster speed.**4.2 Slope**• The slope of a line is the ratio of the “rise” to the “run”. • The steepness of a line is measured by finding its slope.**4.2 Graphs of changing motion**• Objects rarely move at the same speed for a long period of time. • A speed vs. time graph is also useful for showing the motion of an object that is speeding up or slowing down.**On the graph, the length is equal to the time and the height**is equal to the speed. • Suppose we draw a rectangle on the speed vs. time graph between the x-axis and the line showing the speed. • The area of the rectangle is equal to its length times its height. 4.2 Graphs of changing motion Fill In graph**Christopher borrowed his mother’s car to run a quick**errand. Use the graph to answer questions about his trip. How far did Christopher’s car travel between points A and B? How much time did it take for Christopher to travel from point A to point B? Describe the motion of Christopher’s car between points B and C. What is the speed of the car between points A and B? Christopher’s Road Trip**How would you describe the slope of the graph between points**D and E? What does a negative slope tell you about the direction the car is traveling? Is Christopher traveling faster between points A and B or points F and G? How can you tell? What happens at point G?**Chapter Four: Motion**• 4.1 Position, Speed and Velocity • 4.2 Graphs of Motion • 4.3 Acceleration**Section 4.3 Learning Goals**• Define acceleration. • Determine acceleration by mathematical and graphical means. • Explain the role of acceleration in describing curved motion and objects in free fall.**Key Question:**What is acceleration? Investigation 4B Acceleration