Section 11.1, Distance and Displacement Choosing a Frame of Reference –To describe motion, one must decide what the motion is relative to. –In a moving train, the motion could be: Relative to the land if you are looking out the window. Relative to a point in the hallway if you are walking through the car How you describe motion depends on your frame of reference.

Section 11.1, Distance and Displacement How Fast You Are Moving –Relative motion is motion in relation to the chosen frame of reference. When a train moves past a point on the land it seems to be moving very fast, but people in the train looking at each other seem to be motionless. Which Frame Should You Choose Choose the reference frame that is meaningful to the motion you are describing.

Section 11.1, Distance and Displacement Measuring Distance. –Distance is the length of a path between two points. –The SI Unit for measuring distance is the meter (m). The Kilometer ( km, 1000 meters) is used for measuring large distances. The Centimeter (cm,.01 meters) is used for measuring smaller distances.

Section 11.1, Distance and Displacement Measuring Displacements –Displacement is the direction from a starting point and the length of a straight line from the starting point to the ending point. –Although they sound similar distance and displacement are two different things.

Notice the red line. That is the displace- ment from home to school. The yellow line however represents the distance.

Section 11.1, Distance and Displacement Combining Displacements. We use vectors to explain displacements. –Vectors are quantities that have magnitude and direction. The length of a vector’s arrow gives the vectors magnitude. The arrow points in the direction of the motion.

Each of the arrows in the picture represents a vector. It gives a direction and it gives a magnitude (distance).

Section 11.1, Distance and Displacement Combining Displacements Displacement Along a Straight Line –Vectors along a straight line can be added if they are going in the same direction. –Vectors along a straight line going in opposite directions must be subtracted. –Page 330 in textbook.

Section 11.1, Distance and Displacement Combining Displacements –Displacement That Isn’t Along a Straight Path. We use graphing to combine two or more vectors not along a straight line. When we add two or more vectors, we get what is called a resultant vector.

Notice that with this set of vectors that the red line is the resultant vector. The sum of the yellow vectors, it will equal the Magnitude and direction of the red vector.

Section 11.1, Distance and Displacement Combining Displacements

Getting Started Quiz 1 1.A container holds 4 L of gas at a pressure of 300 kPa. If the volume of the container is increased to 6 L, what will be the pressure of the gas in the container? 2.Balance and identify these equations: MgCl 2 + AgNO 3 Mg(NO 3 ) 2 + AgCl Fe + O 2 Fe 2 O 3

Section 11.1 Quiz 1.Motion in relation to a plane of reference is called ________. 2.The SI Unit used to measure distance is the _________. 3.A ______ has both magnitude and direction and is usually expressed with an arrow. 4.When we add 2 or more vectors, we get a _________ ________.

Section 11.1 Quiz 5.We use _______ to explain displacements.

Section 11.2, Speed and Velocity Speed –Speed is the ratio of the distance an object moves to the time it is moving. –Meters per second (m/s) is the SI Unit for speed Average Speed –Average speed is computed for the entire duration of a trip. Avg Speed = Total distance or V = d Total time t

Section 11.2, Speed and Velocity Average Speed Problem: Bubba and his family take a trip to Myrtle beach. The distance from Bubba’s home is 450 miles and it takes them 9 hours to get there. What is the average speed they are driving?

Section 11.2, Speed and Velocity Instantaneous Speed –Instantaneous speed is the rate at which an object is moving at a given moment in time

Section 11.2, Speed and Velocity Graphing Motion –The slope of a graph is the change in the vertical axis value divided by the the change in the horizontal axis value. –In other words, the slope of a distance – time graph is speed (mph, km/s, etc.).

Section 11.2, Speed and Velocity Velocity –Velocity describes both speed and direction of motion. –Velocity is a vector. –If we say an airplane is moving due east at a speed of 600 K/hr, we have used both speed and direction of motion to describe a velocity.

Section 11.2, Speed and Velocity Velocity Since direction and speed both can change in a situation, we will find it necessary to deal with two or more velocities (vectors) when working problems.

Section 11.2, Speed and Velocity Combining Velocities –Two or more velocities can be added by vector addition.

Notice the diagram

Section 11.2, Speed and Velocity

Getting Started, Quiz 2 1.Balance and identify the following equations: Cu + AgNO 3 Cu(NO 3 ) 2 + Ag CH 4 + O 2 CO 2 + H 2 0 A Container holds 4 L of a gas at a temperature of 27 o C, If its volume changes to 2 L, what will its temperature be?

Section 11.3, Acceleration What Is Acceleration? Acceleration is the rate at which velocity changes. –Remember, velocity is a combination of speed and direction, so acceleration can occur because of: Changes in speed Changes in direction Changes in both speed & direction

Section 11.3, Acceleration What Is Acceleration? –Acceleration is usually expressed in meters per second squared (m/s 2 ). –Acceleration due to gravity (for dropped objects is 9.8 m/s 2. Changes in speed –Driving on the interstate at a constant speed of 70 mph you are not accelerating, but when you increase the speed to 90 mph, you are accelerating.

Notice that as the rock drops in the well, it falls faster (9.8 m/s) faster with each passing second. This represents a constant acceleration due to gravity which affects all falling objects giving us the constant acceleration due to gravity of 9.8 m/s 2. Remember, acceleration refers to a change in velocity. This example only applies to bodies in “free fall”.

Section 11.3, Acceleration What Is Acceleration? –Changes in Direction When you ride a bicycle around a curve, your speed can remain the same, but your change in direction means you are accelerating. (You are accelerating in a new direction.)

Section 11.3, Acceleration What Is Acceleration? –Changes In Speed and Direction When you ride a rollercoaster, you are changing both speed and direction, thus you are accelerating.

Section 11.3, Acceleration What Is Acceleration? Constant Acceleration –When an object experiences constant acceleration, two things must be occurring. First, the object must be moving in a straight line. Second, its velocity must be changing at a constant rate. (It increases by the same amount each second)

Section 11.3, Acceleration Calculating Acceleration Straight Line Motion –Use the equation: Acc = V f – V i – t –Acc = acceleration –V f = final velocity –V i = initial velocity –t = time

Section 11.3, Acceleration Graphs of Accelerated Motion –Acceleration can be either positive (speeding up) or negative (slowing down) –When we plot acceleration on a graph, we plot speed (the vertical “y” axis) against time (the horizontal “x” axis). –Remember, acceleration involves a change in speed, either an increase or decrease.

The graph to the left illustrates positive acceleration, while the graph on the right illustrates negative acceleration

Section 11.3 Acceleration Graphs of Accelerated Motion –Distance – Time Graphs On distance-time graphs, acceleration is represented by a curved line. On the next page, notice how the of a ball being dropped curves upward. The upward curve means that as time passes the ball is accelerating (going faster)

Section 11.3 Acceleration Instantaneous Acceleration –Instantaneous acceleration is how fast the velocity of an object is changing at a specific instant.