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Chapter 11 Motion

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**11.1 Distance & Dispalcement**

Motion

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Describing Motion Two parts of describing motion 1. Speed 2. Direction

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**Relative Motion Frame of Reference**

Definition - A system of objects that are not moving with respect to one another Relative Motion Definition – Movement in relation to a frame of reference For example, does a person sitting on a moving train have motion? It all depends on the frame of reference To describe motion accurately and completely, a frame of reference is necssary. Are you moving right now? - It depends on your frame or reference. You are sitting in a school on Earth, Earth is rotating around the Sun, our solar system is rotating around the Milky Way Galaxy and our Galaxy is literally flying through space, moving in an ever-expanding universe. So, whether or not you are moving is a question that must be considered using a frame of reference.

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**Tennis Ball Movement & Frame of Reference**

Demonstration

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**Distance The length of a path between two points**

In other words, distance is the length of a path connecting an objects starting point and its ending point SI unit for distance is the meter

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Displacement Definition – The direction from the starting point and the length of a straight line from the starting point to the ending point Example – What would your displacement be if you rode a rollercoaster?

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Baseball Example If you hit a home run in baseball, you would run from home plate, to each of the bases (1 through 3) and then back to home plate. If there is a distance of 30 meters between each of the bases, what is the total distance you run? What is your displacement?

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Vector Definition – A quantity that has both magnitude (size, length or amount) and direction Represented using arrows Displacement is an example of a vector

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**Displacement along a straight line**

When two displacements have the same direction, you can add their magnitudes 4 km E + 2 km E = 6 km E 2 km 4 km 1 2 3 4 5 6 Point out the parts of a vector in displacement values (i.e. 4km = magnitude, E = direction)

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**Displacement along a straight line**

When two displacements have opposite directions, you can subtract their magnitudes 4 km E + 2 km W = 2 km E 2 km 4 km 1 2 3 4 5 6

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**Displacement that is not along a straight line**

When two or more vectors have different directions, they may be combined using graphing. How can you find displacement? Think MATH and TRIANGLES!

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**Work out problem on board**

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**How can we find the resultant vector?**

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**Resultant Vector The vector sum of two or more vectors**

Can be used to show total displacement Points directly from starting point to ending point

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Distance v. Time Graph

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11.2 Speed & Velocity Motion

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**How do we typically measure the speed of a car?**

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Speed The ratio of the distance an object moves to the amount of time the object moves. SI UNIT Meters per second, or m/s

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**Two types of speed Computed for the entire duration of the trip**

Speed may change from moment to moment, but this tells you the average speed over an entire trip Measured at a particular moment in time Example: The speedometer in a car provides instantaneous speed Average Speed Instantaneous Speed

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**Average Speed d v= t Average speed = Or v = average speed**

Total Distance Average speed = Or v = average speed d = total distance traveled t = total time Total Time d v= t

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Average Speed Example 1 While traveling on vacation, you measure the times and distances you travel. You travel 35 kilometers in 0.4 hours, followed by 53 kilometers in 0.6 hours. What is your average speed? d = 35 km + 53 km = 88 km t = 0.4 h h = 1.0 h

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Average Speed Example 2 A person jogs 4.0 km in 32 minutes, then 2.0 km in 22 minutes, and finally, 1.0 km in 16 minutes. What is the jogger’s average speed in kilometers per minute? In km/ hour?

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**Graphing Motion Use can use a distance-time graph to describe motion**

Reminder – SLOPE the change in the vertical axis value divided by the change in the horizontal axis value On a distance-time graph, slope is the change in the distance divided by the change in time (or speed)

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**Velocity A description of both speed and direction of motion**

Velocity, like displacement, is a vector because it has both magnitude and direction

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**Combining Velocities Two or more velocities add by vector addition**

When two velocities have the same direction, you can add their magnitudes

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Train Example A man on the ground observes a train passing by. Through the train windows he sees a man running in the same direction as the train is moving. What is the apparent velocity of the man running on the train if the train is moving at 30 km/h and the man is running at 5 km/h?

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5 km/h 35 km/h

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Plane Example A plane is moving south at 100 km/hour. Wind is blowing from the east at 25 km/ hour. What is the resultant velocity of the plane? (HINT – draw a picture to help visualize the problem)

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**Warm-up Activity (Vector Addition)**

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11.3 Acceleration Motion

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**What is acceleration? The rate at which velocity changes Changes in:**

Speed Direction Or both speed & direction Acceleration is a vector (it has both magnitude and direction)\ SI Unit – meters per second per second (m/s2)

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**Deceleration An acceleration that slows an objects speed**

Negative acceleration Example As your car approaches a red light you step on the break pedal to slow the car down. This causes the velocity of the car to change (it decreases) and thus the car decelerates.

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Free Fall The movement of an object toward Earth solely because of gravity Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s2

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Free Fall (Continued) t = 0s v = 0 m/s Each second an object is in free fall, its velocity increases downward by 9.8 m/s t = 1s v = 9.8 m/s t = 2s v = 19.6 m/s t = 3s v = 29.4 m/s

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Changes in Direction You can accelerate even if your speed is constant because acceleration also includes changes in direction Example If you ride a bike around a curve and maintain the same speed, acceleration changes because your direction changes

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**Roller Coasters… Green Lantern Front Seat (Six Flags)**

Describe the acceleration of the roller coaster as it reaches and just overcomes the first hill.

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**Constant Acceleration**

A steady change in velocity The velocity of an object moving in a straight line changes at a constant rate

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**Calculating Acceleration**

For straight-line motion: Change in Velocity Acceleration = Total Time A = t vf - vi vf = Final Velocity vi = Initial Velocity

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**Acceleration Example #1**

t = 0s v = 0 m/s What is the magnitude of the skydiver’s acceleration after 1 second? Between 2 and 3 seconds? t = 1s v = 9.8 m/s t = 2s v = 19.6 m/s t = 3s v = 29.4 m/s

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**Acceleration Example #2**

A ball rolls down a ramp, starting from rest. After two seconds, its velocity is 6 m/s. What is the acceleration of the ball? A = t vf - vi

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vf = ? vi = ? t = ? A = t vf - vi

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**Group Practice Activity**

Complete the problem assigned to your group. You will be presenting your answer to the class.

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**A car traveling at 10 m/s starts to decelerate steadily**

A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration?

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**An airplane travels down a runway for 4**

An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s2. What is its change in velocity during this time.

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**A child drops a ball from a bridge**

A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water? (Hint: Think “FREE FALL”)

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**A boy throws a rock straight up into the air**

A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boy’s hand? (Hint: Think “FREE FALL”)

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**Increasing Acceleration Constant Acceleration Decreasing Acceleration**

Speed-Time Graphs The slope of a speed-time graph is acceleration What is the formula for slope of a line? Speed Speed Speed Time Time Time Increasing Acceleration Constant Acceleration Decreasing Acceleration

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**Instantaneous Acceleration**

How fast a velocity is changing at a specific instant

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11.3 Warm-up Speed-time graph

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In the warm-up/ journal section of your binder sketch a speed-time graph of a car starting from rest, accelerating up to a speed limit of 35 mph, maintaining that speed for 10 seconds, then slowing again to a stop at a red light.

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