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

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.

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.  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.

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.

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.

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

4.1 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?

4.1 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?

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

4.1 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.

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  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?

4.1 Vectors on a map  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  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

4.1 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

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.