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**Chapter 2 Physical Science**

Motion Chapter 2 Physical Science

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Motion Objectives 1. Distinguish between distance and displacement. 2. Distinguish between speed and velocity. 3. Interpret motion graphs. 4. Identify how acceleration, time and velocity are related. 5. Explain how positive and negative acceleration affect motion. 6. Solve problems involving time, distance, velocity, and acceleration.

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**How do we know an object is moving?**

An object moves if its position changes against some background that stays the same. -this unchanging background is called the reference frame or reference point -examples of reference points: trees, posts, buildings motion: when an object changes position over time when compared with a reference point

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**distance: total length of a path between two points **

In describing motion, it is important to know how far an object has moved. distance: total length of a path between two points -does not have to be a straight line -unit is the meter You also need to know the direction you are going… Finish Start

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**displacement: direction from the starting point to the ending point in a straight line**

-states how far (distance) away an object is from a given point and in what direction the object is from that point. -example of a vector, a quantity that has magnitude (size, length, amount) and direction

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Vectors You can add or subtract displacements by vector addition or subtraction. -vector addition: when going same direction -vector subtraction: when going opposite directions

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**Vector Practice For each of the following:**

a. draw a picture showing motion b. determine the total distance traveled c. calculate the displacement. A sprinter runs 5 km north and 7 km south. A cyclist travels 200 m west and 100 m east. A truck travels 1 mi east, 2 mi south and 1 mi west.

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Motion Quiz 1

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**Speed Do all objects move at the same speed?**

speed: distance an object moves to the amount of time the object is in motion. -measured in meters/second (m/s)

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**There are three ways to describe speed:**

1. instantaneous speed: speed measured at a particular moment. -radar gun, speedometer 2. constant speed: speed that remains the same the entire trip. -the object does not speed up or slow down -shown by a straight line on a distance-time graph (we will look at these shortly)

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**3 . average speed: speed computed for the entire trip**

- average speed = total distance total time v = d t Example 1: If you traveled 200 miles in 3 hours, your average speed was 66.7 mi/hr.

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**Using the speed formula**

Example 2: If a student ran 5 kilometers in 2 hours, what would his/her speed be? Step 1: write the known variables d = distance = 5 km t = time = 2 hrs Step 2: write the unknown variable v = speed = ? km/hr You MUST show the units in both the problem and the answer!!

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**Using the speed formula**

Example 2: If a student ran 5 kilometers in 2 hours, what would his/her speed be? Step 3: write the formula needed v = d t Step 4: plug in the numbers with their units v = 5 km 2 hr You MUST show the units in both the problem and the answer!!

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**Using the speed formula**

Example 2: If a student ran 5 kilometers in 2 hours, what would his/her speed be? Step 5: Calculate answer showing all work. You may need to show how you rearranged the equation to show how you got the answer. v = 2.5 km/hr You MUST show the units in both the problem and the answer!!

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**Using the speed formula**

Example 3: If a cheetah runs 20 miles per hour in 0.15 hours, how far does it travel? Step 1: write the known variables v = speed = 20 mi/hr t = time = 0.15 hrs Step 2: write the unknown variable d = distance = ? mi You MUST show the units in both the problem and the answer!!

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**Using the speed formula**

Example 3: If a cheetah runs 20 miles per hour in 0.15 hours, how far does it travel? Step 3: write the formula needed v = d t Step 4: plug in the numbers with their units 20 mi/hr = d 0.15 hr You MUST show the units in both the problem and the answer!!

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**Using the speed formula**

Example 3: If a cheetah runs 20 miles per hour in 0.15 hours, how far does it travel?? Step 5: Calculate answer showing all work. 20 mi/hr = d 0.15 hr (0.15hr) 20 mi/hr = d (0.15 hr) d = 3 mi You MUST show the units in both the problem and the answer!!

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Speed Practice 1 You must show the given information, formula, units and work!!! 1. A car traveling at a constant speed covers a distance of 750m in 25s. What is the car’s speed? 2. The cheetah, the fastest of land animals, can run a distance of 274m in 8.65s at its top speed. What is that top speed? 3. A cat runs from a dog at a speed of 3 m/s. If the cat runs for 10 seconds, how far has it run? 4. An apple falls 2 meters from a tree at a speed of 1.5 m/s. How long did it take the apple to fall?

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Motion Review 1 1. How do we know that motion has occurred? 2. What is a vector? 3. Give two objects that can be used for a frame of reference. (You cannot use the ones in your notes) 4. What are the SI units for a. distance b. speed? 5. What is the difference between distance and displacement? 6. How do we calculate speed? 7. Contrast instantaneous speed, average speed and constant speed.

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Homework 1 Show all work & units!! 1. A plane flies 4000 miles in 5 hours. What is its speed? 2. A car travels from 20 meters to 60 meters in 10 seconds. What is its speed? 3. A car travels 60 m/s for 8 seconds. How far does it travel? 4. If it takes you 6.5 meters to stop when you are traveling 65 m/s, how long does it take you to stop? 5. A dog travels 3 blocks south, turns around and travels 2 blocks north. What is its displacement?

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Motion Quiz 2

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Distance-Time Graphs What is the dependent variable and the independent variable? Calculate the slopefor each of the three graphs. Be sure to label each problem with the correct graph and show the units.

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**Distance-Time Graph Answers**

Constant High Speed: slope = rise/run = 250m/10s = 25 m/s Constant Low Speed: slope = rise/run = 125m/10s = 12.5 m/s Varying Speed: slope = rise/run = 500m/20s = 25 m/s

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**Distance-Time Graph Answers**

What does the slope of a distance-time graph show? slope = rise/run = d/t = speed (v)

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**Distance-Time Graph Answers**

On a distance-time graph: A linear (straight) line shows constant speed. A flat line shows no speed (stopped) graph

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**Velocity Is knowing the speed of an object always enough?**

No. Sometimes you must know the speed and direction the object is traveling, which is known as velocity. -velocity is positive in the direction of motion (a negative velocity means that the object is traveling in the opposite direction.) Ex. speed: 55 mi/hr ; velocity: 55 mi/hr South

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Velocity constant velocity occurs when an object is traveling at the same speed and direction. -if at any time the object changes direction, it changes the velocity. Note: velocity is calculated using the same formula for speed (v = d/t), however be sure to state the direction when asked for velocity!

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Motion Review 2 Write the Q and A 1. What does a negative and positive velocity mean? 2. How does velocity differ from speed? 3. What are the units for speed? For velocity? 4. What causes an object to change velocity? There are two causes. 5. Is knowing the speed of an object always enough? 6. How do you know if a distance-time graph shows if the speed is constant?

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Homework 2 Complete the worksheet handed out in class. You may write on the worksheet.

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Motion Quiz 3

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**Copy the following on a separate sheet of paper.**

Speed of a Cart Lab Copy the following on a separate sheet of paper. Purpose: You will measure the stopping distance and the time required for your cart to come to a complete stop using various heights of a ramp. Materials: 2 books, cart, whiteboard and marker, stopwatch, meter stick Procedure: 1. Using a ruler, draw a line to mark a starting point for your cart. 2. Prop the whiteboard up with one book. 3. Placing the cart at the starting point, let it roll down the ramp and come to a complete stop. Do not push the cart. 4. As soon as the front tires hit the bottom of the ramp, start the stopwatch and stop it when the cart comes to a complete stop. Record the time in your data table.

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**Copy the following on a separate sheet of paper.**

Speed of a Cart Lab Copy the following on a separate sheet of paper. 5. Using a meter stick or tape measure, measure the distance from the bottom of the ramp to the front tires of your cart. This is your stopping distance. Record in the data table. 6. Repeat steps 3-5 five times, each time recording data into your data table. 7. Using the formula in your data table, calculate the velocity of the cart for each of the 5 trials. Leave room beneath your data table to show all work. 8. Calculate the average distance and average speed of the truck. 9. Repeat steps 2-7 with two textbooks. 10. Draw a graph using your average velocity and the average distance traveled. You will have 2 lines on the graph, so be sure to label each line (1 book or 2 books).

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Speed of a Cart Lab Data Table: Use a ruler to copy this table two times (one for each set of books), leaving room to show calculations below each table. Data Table 1: 1 book Trial d (cm) t (s) v (cm/s) 1 2 3 4 5 average

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**(Be very detailed and specific)**

Speed of a Cart Lab Analysis: Explain the relationship between stopping distance and the speed the cart is going. Discuss how changing the height of the ramp affects both the speed and stopping distance. Use your data to explain. You should have a good 6-8 sentences. (Be very detailed and specific)

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Speed-Time Graphs The speed an object travels can also be expressed on a graph, gives useful information about the object’s motion. -the slope of the line on a distance-time graph represents the change in distance (m) per the change in time (s); slope = d/t = v -what does the slope of the line of a speed-time graph represent?

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Speed-Time Graphs 2. Describe the speed of the object shown on the graph. 3. How would I calculate the slope of this graph? Show the formula and how you determined the slope. 1. What is the dependent variable? The independent variable?

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**Speed-Time Graphs Slope = rise = speed (m) run time (s)**

What does the slope of speed/time show? acceleration: rate at which velocity changes over time. -can be described as a change in speed, direction or both -is also a vector (like displacement and velocity) -calculated in meters per second per second (m/s2) .

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Acceleration A positive acceleration is an increase in velocity, as shown by a positive slope. A negative acceleration is a decrease in velocity, as shown by a negative slope. -the horizontal line represents constant velocity (speed) and zero acceleration.

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**Acceleration: Velocity-Time Graphs**

Straight lines in both graphs represent constant acceleration. The slope of a velocity-time graph gives acceleration.

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**Acceleration: Distance-Time Graph**

A straight line on a d-t graph shows constant motion. What does the curved (nonlinear) line on a d-t graph show? -accelerated motion. -in this case, a positive slope means the object is speeding up

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Motion Review 3 1. What does the slope of a distance-time graph give? A velocity-time graph? 2. What do we mean by positive and negative acceleration? 3. For acceleration to occur, what two possible changes must be made? 4. What are the units for acceleration? 5. Describe the object’s motion at each interval (A to B, etc.)

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Homework 3 Complete the worksheet handed out in class. You may write on the worksheet.

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**Acceleration-Formula**

acceleration = final velocity – initial velocity time a = vf – vi t or acceleration = change in velocity time a = v t = “change”

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**Using the acceleration formula**

Example 1: A flowerpot falls from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. What is the acceleration of the flowerpot? Step 1: write the known variables t = time = 1.5 s v = velocity = 14.7 m/s Step 2: write the unknown variable a = acceleration = ? m/s2 You MUST show the units in both the problem and the answer!!

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**Using the acceleration formula**

Example 1: A flowerpot falls from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. What is the acceleration of the flowerpot? Step 3: write the formula needed a = Dv = vf-vi t t Step 4: plug in the numbers with their units a = 14.7 m/s – 0.0 m/s 1.5 s You MUST show the units in both the problem and the answer!!

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**Using the acceleration formula**

Example 1: A flowerpot falls from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. What is the acceleration of the flowerpot? Step 5: Calculate answer showing all work. a = 14.7 m/s 1.5s a = 9.8 m/s2 You MUST show the units in both the problem and the answer!!

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**Using the acceleration formula**

Example 2: What is the time it took a plane to go from 200 m/s to 100 m/s if its acceleration is -20m/s2? Step 1: write the known variables a = acceleration = -20m/s2 vf = 100 m/s vi = 200 m/s Step 2: write the unknown variable t = time = ? s You MUST show the units in both the problem and the answer!!

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**Using the acceleration formula**

Example 2: What is the time it took a plane to go from 200 m/s to 100 m/s if its acceleration is -20m/s2? Step 3: write the formula needed a = Dv = vf-vi t t Step 4: plug in the numbers with their units -20m/s2 = 100 m/s – 200 m/s t You MUST show the units in both the problem and the answer!!

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**Using the acceleration formula**

Example 2: What is the time it took a plane to go from 200 m/s to 100 m/s if its acceleration is -20m/s2? Step 5: Calculate answer showing all work. -20m/s2 = 100 m/s – 200 m/s = -100 m/s t t (t)-20m/s2 = -100 m/s (t) t You MUST show the units in both the problem and the answer!!

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**Using the acceleration formula**

Example 2: What is the time it took a plane to go from 200 m/s to 100 m/s if its acceleration is -20m/s2? Step 5: Calculate answer showing all work. (t)-20m/s2 = -100 m/s -20m/s m/s2 t = 5 s You MUST show the units in both the problem and the answer!!

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Homework 4 1. A jetliner speeds up from 40m/s to 80m/s in 20s. What is the airliners acceleration? 2. An automobile manufacturer claims that its latest model can ‘go from 0 to 90’ in 7.5s. If the ’90’ refers to km/h, calculate the automobile’s acceleration. 3. A ball is dropped from a cliff and has an acceleration of 9.8m/s2. How long will it take the ball to reach a speed of 24.5m/s? 4. A sprinter leaves the starting blocks with an acceleration of 4.5m/s2. What is the sprinter’s speed 2s later?

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Motion Quiz 4

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Motion Review 4 1. Are the following statements true? Why or why not? a. “You can determine your speed at the midpoint of a trip by calculating the average speed for the entire trip.” b. “If a car travels around a curve on a highway at 60km/hr, the velocity does not change.” 2. What is the displacement of a cyclist who travels 1 mile north, 1 mile east, then 1 mile south? 3. A horse on a carousel that is moving at a constant speed is accelerating because________. 4. In what ways can an object accelerate?

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Homework 5 Complete the worksheet handed out in class. You may write on the worksheet.

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