Quiz Next Week Monday & Tuesday  The name of the COSMOS episode is the 3 rd in the series “When Knowledge Conquered Fear” com/watch?v=YHLV_Z yd64U  Study the notes  Learn to solve for a speed problems & Acceleration problems  See Word Document for possible questions on Quiz

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  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 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

4.2 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 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”.

4.3 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.

4.3 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.

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

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

4.3 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.

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.