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Speed, Velocity and Acceleration Measuring motion Slide 2 Slide 3 Measuring Distance Meter international unit for measuring distance. = 50 m 1 mm Slide 4 We use the variable speed to describe how quickly something moves. Saying a race car, runner, or plane is fast is not enough to accurately describe its speed scientifically. Slide 5 The speed of a bicycle is the distance it travels divided by the time it takes. Slide 6 Constant means does not change so constant speed is speed that does not change. How do we know the speed of the bike is constant? Slide 7 Since speed is a ratio of distance over time, the units for speed are distance units over time units. Slide 8 An equation can be used to calculate speed, distance, or time if two of the three values are known. Slide 9 Calculating Speed Speed (S) = distance traveled (d) / the amount of time it took (t). S = d/t Slide 10 Units for speed Depends, but will always be a distance unit / a time unit Ex. Cars: mi./h Jets: km/h Snails: cm/s Falling objects: m/s Slide 11 Calculating speed If I travel 100 kilometers in 1 hour then I have a speed of 100 km/h If I travel 1 meter in 1 second then I have a speed of. 1 m/s S = d/t Slide 12 The speed found by dividing the total distance by the total time is the average speed. Slide 13 Average speed Speed is usually NOT CONSTANT Ex. Cars stop and go regularly Runners go slower uphill than downhill Average speed = total distance _________________ total time Slide 14 Calculating Average Speed It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets. Total Distance: 40 km + 20 km = 60 km Total Time: 1 h + 2 h = 3 hr Ave. Speed: total d/total t = 60 km/3 h = 20 km/h Slide 15 Question I jogged 100 m in 60 seconds. I then ran another 100 m uphill in 60 seconds. What is my average speed? A) 100 /min B) 2000 m/min C) 100 m/min D) 200 m/min E) 20 m/min Total Dist. = 100 m + 100 m = 200 m Total Time = 60 s + 60 s = 120 s = 2 min Ave speed = total dist/total time = S = 200 m / 2 min = 100 m/ min Slide 16 How fast is a snake moving that can slither 20 meters in 5 seconds? Slide 17 It takes Brooke 20 minutes to run 100 meters. What is her speed in meters per minute? It took Grandma 1.5 hours to drive 150 kilometers from her house to mine. How fast was she driving? Slide 18 Velocity Velocity SPEED with DIRECTION of an object. Example: An airplane moving North at 500 mph A missile moving towards you at 200 m/s Slide 19 Question What is the difference between speed and velocity? Speed is just distance/time. Velocity also includes direction. Slide 20 Slide 21 Slide 22 1. Calculate the average speed of a car that travels 280 km in 4 hours. 2. You ride your bicycle at an average speed of 15 km/h for 2 hours. How far did you go? 3. How long will it take you to run 100 meters if you run at 5 m/s? Some practice Slide 23 More Practice... If a car drives 490 miles in 6 hours, how fast did it drive? If a rocket flies 17,000 miles per hour for 12 hours, how far will it go? If an airplane flies 800 miles at 300 miles per hour, how long will it take them to get there? Slide 24 Comparing Variables In order to compare variables they must be in the same units. To convert between units, you multiply and/or divide by conversion factors. A conversion factor is an equivalent ratio. Slide 25 Using conversion factors Conversion factors are translators between one language of units and another. Slide 26 Velocity: Direction Matters Velocity is the speed of an object in a particular direction. Do not use velocity and speed in the same way because they are NOT the same thing! Slide 27 The difference between speed and velocity is DIRECTION! Slide 28 Velocity will always include a direction! The velocity of a plane headed to California might be 600 km/h west. The velocity of a train headed to New York might be 90 km/h north. Slide 29 Which are examples of velocity? 1. 25 m/s forward 2. 1,500 km/hr 3. 55 m/s south 4. 75 cm/s down 5. 60 mph Slide 30 How to combine velocities If 2 velocities are going in the same direction, add them together. If 2 velocities are going in opposite directions, subtract the smaller from the larger. The resulting direction will continue to be that of the larger velocity. Slide 31 Velocity Practice A car travels with a velocity of 20 m/s to the west. An insect inside the car flies with a velocity of 2 m/s to the east. What is the resultant velocity of the insect? Dont forget, your answer must include a direction!! Slide 32 More Velocity Practice A bus is traveling forward at 30 km/h. You get up from your seat and walk toward the driver at a speed of 2 km/h. What is your resultant velocity? Slide 33 Velocity will change if : 1. The direction of travel changes: Example: A plane takes off to the east and then makes a turn to head northit has changed velocity. 2. The speed of travel changes: Example: The car slows down to leave the highway to go down an exit ramp. Slide 34 Graphing Speed: Distance vs. Time Graphs Phoenix Denver Slide 35 Graphing Speed: Distance vs. Time Graphs Slide 36 3 hr 600 km Slide 37 Graphing Speed: Distance vs. Time Graphs 3 hr 600 km Slide 38 Question What does the slope of a distance vs. time graph show you about the motion of an object? It tells you the SPEED Slide 39 Question Below is a distance vs. time graph for 3 runners. Who is the fastest? Leroy is the fastest. He completed the race in 3 hours Slide 40 Acceleration Acceleration = speeding up Acceleration the rate at which velocity changes Can be an: Increase in speed Decrease in speed Change in direction Slide 41 Types of acceleration Increasing speed Example: Car speeds up at green light Decreasing speed Example: Car slows down at stop light Changing Direction Example: Car takes turn (can be at constant speed) screeeeech Slide 42 Question How can a car be accelerating if its speed is a constant 65 km/h? If it is changing directions it is accelerating Slide 43 Calculating Acceleration If an object is moving in a straight line Units of acceleration: m/s 2 Slide 44 Calculating Acceleration 0 s 1 s2 s3 s4 s 0 m/s 4 m/s 8 m/s 12 m/s16 m/s Slide 45 Question A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydivers average acceleration? Slide 46 Graphing Acceleration Can use 2 kinds of graphs Speed vs. time Distance vs. time Slide 47 Graphing Acceleration: Speed vs. Time Graphs 1)Speed is increasing with time = accelerating 2)Line is straight = acceleration is constant Slide 48 Graphing Acceleration: Speed vs. Time Graphs 1)In Speed vs. Time graphs: Acceleration = Rise/Run = 4 m/s 2 s = 2 m/s 2 Run = 2 s Rise = 4 m/s Slide 49 Graphing Acceleration: Distance vs. Time Graphs 1)On Distance vs. Time graphs a curved line means the object is accelerating. 2)Curved line also means your speed is increasing. Remember slope = speed. Slide 50 Question Above is a graph showing the speed of a car over time. 1) How is the speed of the car changing (speeding up, Slowing down, or staying the same)? 2) What is this cars acceleration? 1)The car is slowing down 2)Acceleration = rise/run = -6m/s 3s = -2 m/s 2 Run = 3 s Rise = -6 m/s Slide 51 Question: 1)Which line represents an object that is accelerating? The black and red lines represent a objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so must be slowing down Remember: in distance vs. time graphs: curved line = accelerating, flat line = constant speed