 MOTION. Chapter Four: MotionMotion  4.1 Position, Speed and Velocity  4.2 Graphs of Motion  4.3 Acceleration.

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MOTION

Chapter Four: MotionMotion  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.

4.1 Position, 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. Distance = 20 cm New position

4.1 Position, Speed and Velocity  The variable speed describes how quickly something moves.  To calculate the speed of a moving object divide the distance it moves by the time it takes to move.

Put these are on your best friend!! Word Map

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 Average speed  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 Instantaneous 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)

How far do you go if you drive for two hours at a speed of 100 km/h? 1.Looking for:  …distance 2.Given:  …speed = 100 km/h time = 2 h 3.Relationships:  d = vt 4.Solution:  d = 100 km/h x 2 h = 200 km = 200 km Solving Problems

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.

Speed

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  If Pathfinder was crawling on a straight board, it would have only two choices for direction.  Out on the surface of Mars, Pathfinder has more choices.  The possible directions include north, east, south, and west, and anything in between.

4.1 Maps and coordinates  A graph using north−south and east−west axes can accurately show where Pathfinder is.  This kind of graph is called a map.  Street maps often use letters and numbers for coordinates.

4.1 Vectors on a map 1Vectors  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 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) d = 2 m/s x 10 s = -20 m New position = (+20, - 20)

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? 1.Looking for:  …train’s new position 2.Given:  …velocity = +100 km/h, east ; time = 4 h  …velocity = -50 km/h, west ; time = 4 h 3.Relationships:  change in position = velocity × time Solving Problems

4.Solution:  1 st change in position:  (+100 km/h) × (4 h) = +400 km  2 nd 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. Solving Problems

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 steepness of a line is measured by finding its slope.  The slope of a line is the ratio of the “rise” to the “run”.

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.

4.2 Graphs of changing motion  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. Fill In graph

Fill in the graphs

Christopher’s Road Trip  Christopher borrowed his mother’s car to run a quick errand. Use the graph to answer questions about his trip. 1.How far did Christopher’s car travel between points A and B? 2.How much time did it take for Christopher to travel from point A to point B? 3.Describe the motion of Christopher’s car between points B and C. 4.What is the speed of the car between points A and B?

5.How would you describe the slope of the graph between points D and E? 6.What does a negative slope tell you about the direction the car is traveling? 7.Is Christopher traveling faster between points A and B or points F and G? How can you tell? 8.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.

Investigation 4B  Key Question: What is acceleration? Acceleration

4.3 Acceleration 1  If your speed increases by 1 meter per second (m/s) for each second, then your acceleration is 1 m/s per second.  Acceleration is the rate at which your speed (or velocity) changes.

4.3 Acceleration 2  Acceleration causes the line to slope up on a speed vs. time graph.  Acceleration is easy to spot on a speed vs. time graph. What is the bike’s acceleration?

4.3 Acceleration 3  If the hill is steeper, the acceleration is greater.

4.3 Acceleration 4  There is zero acceleration at constant speed because the speed does not change.

4.3 Acceleration 5  Speed and acceleration are not the same thing.  You can be moving (non-zero speed) and have no acceleration (think cruise control).  You can also be accelerating and not moving!  A falling object begins accelerating the instant it is released.

Positive and negative Accel.

Speed is the same changing Accel

4.3 Acceleration  Acceleration describes how quickly speed changes.  Acceleration is the change in speed divided by the change in time.

4.3 Speed and acceleration  An acceleration of 20 km/h/s means that the speed increases by 20 km/h each second.  The units for time in acceleration are often expressed as “seconds squared” and written as s 2. Can you convert this rate using conversion factors?

Solving Problems  A sailboat moves at 1 m/s.  A strong wind increases its speed to 4 m/s in 3 s.  Calculate acceleration.

1.Looking for:  …acceleration of sailboat 2.Given:  …v 1 = 1 m/s; v 2 = 4 m/s; time = 3 s 3.Relationships:  a = v 2 – v 1 /t 4.Solution:  a = (4 m/s – 1 m/s)/ 3 s = 1 m/s 2 Solving Problems

4.3 Acceleration on motion graphs  The word “acceleration” is used for any change in speed, up or down.  Acceleration can be positive or negative.

4.3 Acceleration on speed-time graphs  Positive acceleration adds more speed each second.  Things get faster.  Speed increases over time.

4.3 Acceleration on speed-time graphs  Negative acceleration subtracts some speed each second.  Things get slower.  People sometimes use the word deceleration to describe slowing down.

4.3 Acceleration on position-time graphs  The position vs. time graph is a curve when there is acceleration.  The car covers more distance each second, so the position vs. time graph gets steeper each second.

4.3 Acceleration on position-time graphs  When a car is slowing down, the speed decreases so the car covers less distance each second.  The position vs. time graph gets shallower with time.

4.3 Free fall  An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it.  Free Free

4.3 Free fall  Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s 2  The letter “g” is used for acceleration due to gravity.

4.3 Acceleration and direction  Acceleration occurs whenever there is a change in speed, direction, or both.

4.3 Acceleration and direction  A car driving around a curve at a constant speed is accelerating because its direction is changing.

4.3 Acceleration and direction  Individual vectors can be drawn to scale to calculate the change in direction.

4.3 Curved motion  A soccer ball is an example of a projectile.  A projectile is an object moving under the influence of only gravity.  The path of the ball makes a bowl-shaped curve called a parabola.

4.3 Curved motion  Circular motion is another type of curved motion.  An object in circular motion has a velocity vector that constantly changes direction.  X Games X Games

High Tech Animal Trackers  Satellite tagging research studies have led to many new laws and guidelines governing human activities around endangered species.  The more we learn about how animals interact with their environments, the better decisions we can make about how we use the oceans.

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