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Chapter 11 Motion 11.2 Speed and Velocity

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Standards SPS8a. Students will calculate velocity and acceleration

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Distance-Time Graphs The distance traveled by an object in a period of time often is expressed using a line graph. A line graph visually conveys information using sets of data points. Section 11.2 1. Copy the blank graph below on your paper. Complete the graph by plotting the given data points on the graph. Each set of data points represents (time, distance). Note that time is measured in seconds and distance is measured in meters. Connect the plotted points with a straight line. Data points: (0, 0), (2, 40), (4, 80), (6, 120), (8, 160), (10, 200) 2. Describe the motion shown on the graph.

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**Instantaneous speed vs average speed**

Average speed is computed for the entire duration of a trip Instantaneous speed is measured at a particular instant.

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**Speed is the ratio of the distance an object moves to the amount of time the object moves.**

SI unit of speed is meters per second (m/s).

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Average Speed Average speed, is the total distance traveled, d, divided by the time, t, it takes to travel that distance.

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**Calculating Average Speed**

While traveling on vacation, you measure the times and distances traveled. You travel 35 kilometers in 0.4 hour, followed by 53 kilometers in 0.6 hour. What is your average speed?

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**1. A person jogs 4. 0 kilometers in 32 minutes, then 2**

1. A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometer in 16 minutes. What is the jogger’s average speed in kilometers per minute?

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**2. A train travels 190 kilometers in 3**

2. A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average speed?

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Speed 3. At what speed did a plane fly if it traveled 1760 meters in 8 seconds?

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Speed Instantaneous Speed Instantaneous speed, v, is the rate at which an object is moving at a given moment in time.

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**How can you find the speed from a distance-time graph?**

Graphing Motion How can you find the speed from a distance-time graph? The slope of a line on a distance-time graph is speed.

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**Graphing Motion slope = steeper slope = straight line = flat line =**

Distance-Time Graph A B slope = steeper slope = straight line = flat line = speed faster speed constant speed no motion

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**E. Graphing Speed Who started out faster? Who had a constant speed?**

Distance-Time Graph A B Who started out faster? Who had a constant speed? Describe B from min. Find their average speeds.

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Speed vs velocity Velocity is a description of both speed and direction of motion. Velocity is a vector.

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**Two or more velocities add by vector addition.**

Combining Velocities How do velocities add? Two or more velocities add by vector addition.

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**Velocity Practice A car travels 240 km in 3 hours. What is the speed?**

Find the velocity of a swimmer who swims 110 m toward shore in 72 s. Find the velocity of a baseball thrown 38 m in 1.7 s

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**More Velocity Practice**

4. The speed of a cruise ship is 50 km/hr. How far will it travel in 14 hours? 5. Calculate the time in seconds an Olympic skier would take to finish a 2600 m race at an average velocity of 28 m/s?

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Velocity Connection It is 2:00 PM. The weather bureau is tracking a violent storm traveling east at 25 km/hr. It is 75 km west of Suntown. If everyone works until 5:00 PM, will the residents of Suntown be able to get home safely before the storm hits?

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Assessment Questions A woman jogs 10 kilometers in one hour, stops at a restaurant for one hour, and then walks 10 kilometers in two hours. What is her average speed for the outing? 0.2 km/h 4 km/h 5 km/h 10 km/h

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**total distance traveled velocity speed displacement**

Assessment Questions Lisa plotted time on the x-axis of a line graph and distance on the y-axis. What does the slope of her graph represent? total distance traveled velocity speed displacement

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Assessment Questions Lisa plotted time in seconds on the x-axis of a line graph and distance in centimeters on the y-axis. Her plot showed a straight line from (0,0) to (10, 20). What is the speed? 0.5 cm/s 2 cm/s 10 cm/s 20 cm/s

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**Two velocities of an object are combined by using **

Assessment Questions Two velocities of an object are combined by using division of the larger velocity by the smaller velocity. addition of the two speeds. vector addition. numeric addition.

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Assessment Questions A kayak is moving across a stream that is flowing downstream at a velocity of 4 km/h. The kayak’s velocity is 3 km/h. What is the magnitude of the kayak’s velocity relative to the river bank? 1.3 km/h 5 km/h 7 km/h 12 km/h

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**6. The SI unit for speed of an airplane is miles per hour. True False**

Assessment Questions 6. The SI unit for speed of an airplane is miles per hour. True False

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Assessment Questions If you were to sketch a displacement-time graph and a speed-time graph for an object experiencing constant acceleration, what would they look like? Both graphs would be linear, with the displacement-time graph being steeper. Both graphs would be linear, with the speed-time graph being steeper. Both graphs would be nonlinear. The speed-time graph would be linear; the displacement-time graph would be nonlinear.

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Assessment Questions 6. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration. True False

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