 Motion  1 Position, Speed and Velocity  2 Graphs of Motion  3 Acceleration.

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Motion  1 Position, Speed and Velocity  2 Graphs of Motion  3 Acceleration

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, 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.

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

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.

Position, Speed and Velocity  The units for speed are distance units over time units.  This table shows different units commonly used for speed.

Average speed  When you divide the total distance of a trip by the time taken you get the average speed.  On this driving trip around Chicago, the car traveled and average of 100 km/h.

Instantaneous speed  A speedometer shows a car’s instantaneous speed.  The instantaneous speed is the actual speed an object has at any moment.

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

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.

Vectors and velocity  Distance is either zero or a positive value.

Vectors and velocity  We use the term velocity to mean speed with direction.

Keeping track of where you are  Pathfinder is a small robot sent to explore Mars.  It landed on Mars in 1997.  Where is Pathfinder now?

Keeping track of where you are  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?

Keeping track of where you are  Suppose Pathfinder goes backward at 0.2 m/s for 4 seconds. What is Pathfinder’s change in position?

Keeping track of where you are  The change in position is the velocity multiplied by the time.

Keeping track of where you are  Each change in position is added up using positive and negative numbers.  Pathfinder has a computer to do this.

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.

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.

Vectors on a map  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?

Vectors on a map  To get the answer, you figure out your east − west changes and your north − south changes separately. origin = (0, 0)

Vectors on a map  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). d = v x t d = 2 m/s x 10 s = +20 m

Vectors on a map  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

Motion  1 Position, Speed and Velocity  2 Graphs of Motion  3 Acceleration

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.

Constant Speed  Key Question: What do position vs. time and speed vs. time graphs look like for constant speed?

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.

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.

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.

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”.

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.

Graphs of changing motion  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.  On the graph, the length is equal to the time and the height is equal to the speed.

Motion  1 Position, Speed and Velocity  2 Graphs of Motion  3 Acceleration

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.

Acceleration  Key Question: What is acceleration?

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

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

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

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

Acceleration  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.

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

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

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

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

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.

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.

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.

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 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.

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

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

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

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.

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

Studying Two Part Motion  Key Question: What happens to the Energy Car as it travels down a hill and across a flat section of track?

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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