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MOTION • We now know that unbalanced forces can change motion LET’S RACE! JOBS: 3 measurers to make track 4 timers & 4 recorders at 5 meter mark 4 timers & 4 recorders at 10 meter mark 4 timers & 4 recorders at 15 meter mark 1 Hopper 1 Backward walker 1 regular walker 1 Speed walker Let’s Race! NOW WE ARE GOING TO LOOK AT WAYS TO DESCRIBE AND MEASURE MOTION SPEED HOW DO WE DESCRIBE SPEED? HOW FAST SOMETHING GOES How do we CALCULATE SPEED? • How we describe the speed of a CAR: – Miles per hour (MPH) OR – Kilometers per hour (km/h) • What does the miles or kilometers measure? – They are units for distance • What does the hour measure? – It is a unit for time • What does the “per” or “/” mean in math? – division SPEED =RATE that an object moves Distance (D) Rate (speed)= Time (T) Units: Meters/ sec (m/sec) STEPS IN PROBLEM SOLVING STEP 1. Write the formula STEP 2. Substitute given numbers and units STEP 3. Solve for the unknown. SAMPLE PROBLEM: At what speed did a plane fly if it traveled 1760 meters in 8 seconds? SOLUTION Step 1. Question asked “What speed” so use: Rate (Speed) = Distance/Time SOLUTION Step 1. Speed = Distance/Time SOLUTION Step 2. substitute distance = 1760 meters substitute time = 8 seconds Speed = 1760 meters/ 8 seconds SOLUTION Step 1. Speed = Distance/Time Step 2. Speed = 1760 meters/ 8sec SOLUTION Step 3. Do the math to get your answer Speed = 1760m / 8 sec = 220 m/sec SOLUTION Step 1. Speed = Distance/Time Step 2. Speed = 1760 m/ 8 sec Step 3. Speed = 220 m/sec VELOCITY AND ACCELERATION VELOCITY SPEED IN A GIVEN DIRECTION D V EX) 88 km / hr southwest = T AND direction A bird flies south at 20 m/s. • SPEED = 20 m/s • VELOCITY = 20 m/s south CONSTANT VELOCITY -SAME SPEED AND -SAME DIRECTION ACCELERATION happens when VELOCITY IS CHANGING change in Speed and/or Direction Units = meters per sec per sec SPEEDING UP SLOWING DOWN CHANGING DIRECTION CHANGING VELOCITY= ACCELERATION NEED AT LEAST 1 THING DIFFERENT SPEED DIRECTION DIFFERENT DIFFERENT SAME DIFFERENT DIFFERENT SAME Speeding up = POSITIVE ACCELERATION 0 Slowing down = NEGATIVE ACCELERATION A.K.A. DECELERATION DECELERATION • decrease in velocity • negative acceleration • slows down CIRCULAR MOTION Why is object is accelerating even with constant speed? because direction is changing Does it have constant velocity? No ACCELERATION Rate of change in velocity A= Final velocity – Original Velocity Time Change in velocity divided by the time during which this change occurs Acceleration = Time = VF - VI Acceleration VF - VI t A roller coaster’s velocity at the top of the hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26 m/s. What is the acceleration of the roller coaster? SOLUTION: A= A= Final Velocity – Original Velocity Time 26 m/s- 10 m/s 2s A= 16 m/s 2s A= 8 m/sec/sec Velocity vs Time - Acceleration Distance vs Time - Acceleration 500 Velocity (m/s) Distance (meters) 600 400 300 200 100 0 0 1 2 3 4 5 6 7 8 9 180 160 140 120 100 80 60 40 20 0 0 10 1 2 3 4 600 600 500 500 400 300 200 0 5 6 10 200 0 4 9 300 100 3 8 400 100 2 7 Velocity vs Time - Negative Acceleration Velocity (m/s) Disatnce (meters) Distance vs Time - Negative Acceleration 1 6 Time (min) Time (seconds) 0 5 7 8 9 0 1 2 3 4 5 6 Time (min) Time (min) MOTION GRAPHS 7 8 9 10 Velocity vs Time - Constant Speed 80 70 60 50 40 30 20 10 0 Velocity (m/s) Distance (m) Distance vs Time - Constant Speed 0 1 2 3 Time (min) 4 5 16 14 12 10 8 6 4 2 0 0 1 2 3 4 5 Time (min) 6 7 8 9 10 A car accelerated from 0 m/sec to 30 m/sec in 10 sec. What was the rate of acceleration? 3 m/sec/sec A roller coaster is moving at 25 m/sec at the bottom of a hill. Three sec. later it reaches the top of the next hill, moving at 10 m/sec. What is the deceleration of the roller coaster? - 5 m/sec/sec A train accelerated from 5 km/hr to 55 km/hr in 0.5 hr. What was the rate of acceleration? 100 km/hr/hr Definitions: A change in position in a certain amount of time is __________. __________________ is the rate at which an object moves and is determined by dividing ____________ by _____________. _________________________ is speed that does not change. _________________________ is calculated by dividing the total distance by the total time. CONSTANT SPEED SPEED THAT DOES NOT CHANGE CONSTANT SPEED Distance (km) Michelle Goes on a Bike Ride 5.Describe the motion shown in the graph 80 70 60 50 40 30 20 10 0 6.How many different rates are shown? Label them using A, B, . . . . . 1 2 3 4 5 6 Time (hours) 7. Calculate the speeds for the different segments of the journey (Hint - you will have to use change in distance!) Time (hours) A B C D Distance (km) Speed (min/km) 8. What is the average speed for the entire trip? How does the value compare to your calculations above? 9. Can you predict how far Michelle will travel if she travels for another 2 hours? Why or why not? What additional information do you need? Distance (km) Michelle Goes on a Bike Ride 5.Describe the motion shown in the graph (moving at varying speed) 80 70 60 50 40 30 20 10 0 1 2 3 4 5 6 6.How many different rates are shown? Label them using A, B, . . . . . 4 different rates 3 if you notice A and D are same Time (hours) 7. Calculate the speeds for the different segments of the journey (Hint - you will have to use change in distance!) Time (hours) A (1 h) B (1h) C (2 h) D (1h) Distance (km) 10 0 40 10 Speed (km/h) 10 0 20 10 8. What is the average speed for the entire trip? How does the value compare to your calculations above? 11.7 (from graph) or 12 km/h (from math) 9. Can you predict how far Michelle will travel if she travels for another 2 hours? Why or why not? What additional information do you need? no, not constant rate but can get estimate using average speed; need more rates 1. A runner moving eastward covers a distance of a 100 meters in 10 seconds. What is his velocity? Given: D= 100 m 1.Formula 2.Work 3.Answer T= 10s dir= East V= d/t with dir V= 100m/10s East V= 10m/s East 2. A tropical disturbance spotted east of the Philippines was moving at 60 km per hour at a Northwesterly direction and having maximum sustained winds of 150 km/h? What is the storm’s velocity? Given: S= 60km/h dir= NW 1.Work/Answer V= 60km/h NW 3. Seve is walking to a friend’s house. He walks 500m for 10 minutes, then realizes he forgot something important to bring. He turns around, and hurries back to his house. The walk/jog back takes him 5 minutes. Given: Total D= 500m + 500m = 1,000m Total T= 10min + 5 min= 15min x 60 sec/min = 900 sec T= 10 min D= 500m D= 500m T= 5 min 3. Seve is walking to a friend’s house. He walks 500m for 10 minutes, then realizes he forgot something important to bring. He turns around, and hurries back to his house. The walk/jog back takes him 5 minutes. a. What was his average speed in m/sec? Given: Total D= 500m + 500m = 1,000m Total T= 10min + 5 min= 15min x 60 sec/min = 900 sec (15 min) 1.Formula Ave S = total D/total T 2.Work Ave S = 1,000m/900s 3.Answer Ave S = 1.1 m/s 3. Seve is walking to a friend’s house. He walks 500m for 10 minutes, then realizes he forgot something important to bring. He turns around, and hurries back to his house. The walk/jog back takes him 5 minutes. b. What was Seve’s velocity (in m/s) while walking to his friend’s house? Given: D= 500m T= 10min x 60 sec/min= 600 sec dir = forward (to his friend’s house) 1.Formula V= d/t with dir 2. Work V= 500m/600s to friend’s house 3. Answer V= 0.83 m/s to friend’s house 4. Sean is running around the track oval. The oval is 800m long. He is running at a constant speed. It takes him 180 s to complete the track and get back to where he started. a. What is Sean’s speed in m/s? Given: d= 800 m t= 180 s running at constant speed a. What is Sean’s speed in m/s? Given: d= 800 m t= 180 s running at constant speed 1. Formula S= d/t 2. Work S= 800m/180s around oval 3. Answer S= 4.44 m/s If Sean is running at constant speed, is he also moving at constant velocity ? No, he is always changing direction (running around the oval).