Linear Motion Supplemental Textbook Materials Chapter 12 Pages 262 276 Review Questions 4 7 8 10 11 15 16 17 Study of Motion Aristotle Student of Plato Tutor of Alexander Motion ceased when objects in their proper place Thought speed depended on weight Ignored friction air resistance Influential for 2000 years Study of Motion Galileo Studied Copernicus work of 1543 Speed not dependent on weight only on amount of time for falling Galileo s investigation of motion Speed not dependent on weight only on amount of time for falling Noted that gravity increased speed of falling objects decrease speed of rising objects Defined inertia keep moving in same direction and speed without outside influences Galileo s investigation of motion Surface area changes air resistance Objects reach terminal velocity due to air resistance In vacuum this is not a factor Galileo s inclined planes Balls roll down faster and faster Roll up slower and slower Galileo s inclined planes Rises to same height as it is released Height not dependent on incline Study of Motion Speed how fast Velocity how fast and what direction Acceleration how fast it is changing how fast Speed distance speed time 320km 4h 80km h Distance equation Rate time distance Keep units with numbers so you know you have set up the problems correctly Example of speed calculation 80km 4h 320km h Notice that hours cancels because it is above and below the fraction bar Common units of speed Miles per hour mph mi h Kilometers per hour km h Meters per second m s Speed of cheetah 100m 4s 50m 2s 25m s Car traveling 60 km h for 4 h 60km 4h 240km h 60 km h for 10 h 60km 10h h 600km Speed and Velocity Acceleration Change in velocity Acceleration Time interval CHANGE of speed over time not the RATE of speed RATE OF CHANGE Examples of acceleration 45mi 20mi Driving on Monmouth Avenue at 20 mi h h h Increase to 45 mi h in 25 mi 25 seconds change h in speed is 25mi h Divide change of a 1 mi h s speed by time 25s 25mi 11 2m and h s 11 2m s m a 0 44 2 25s s Rate of change of speed Find how much you change v Then divide by amount of time over which the change occurs a 45mi 20mi h h 25mi h 25mi h 1mi h s 25s 11 2m s m a 0 44 2 25s s Rate of change of speed Car can go from stopped to 90 km h in 10 seconds Be sure to REDUCE to lowest terms 90km 25m hr s 90km h 10 s 9km h s 25m s m 2 5 2 10 s s Rate of change of speed Car goes from 60 km h to 65 km h in 2 5 seconds First find amount of change Then divide by time 5km 1 39m hr s 5km h 2km h s 2 5s 1 39m s m 0 55 2 2 5s s Rate of change of speed Bicycle goes from rest to 5 km h in 2 5 seconds 5km h 2km h s 2 5s 1 39m s m 0 55 2 2 5s s Galileo s Inclined Planes Acceleration same for each second of travel Picks up speed faster on steeper inclines Free falling objects Acceleration Neglect air resistance for these equations a v t v at acceleration is velocity divided by time velocity acquired is acceleration multiplied by time Acceleration of Gravity 9 83 m s2 Round off to 10 m s2 Acceleration of Gravity Free fall of object Time elapsed Speed increases seconds 10 m s for every second of fall 0 10 m s 10m 1 s s2 2 Speed meters second 0 10 20 3 30 4 40 Problems If a rock is rock is pried loose from a cliff by frost wedging what is its speed 3 5 seconds after it starts falling After 6 seconds After 100 seconds Solution a v gt 10m v 2 3 5s s g 10m s 2 t 3 5s v 35m s Solution b v gt 10m v 2 6 s s g 10m s 2 t 6s v 60m s Solution c v gt g 10m s 2 t 100s 10m v 2 100 s v 1000 m s s v 3600km h 2236mi h Acceleration Rate of increase or decrease of a rate d t t Changes rate for each increment in time that has passed So there is an increased or decreased distance for each successive time interval Distance g acceleration of gravity a 10m s2 t lower case for time T upper case means Temperature 1 2 1 10m 2 d gt d 2 t 2 s 2 Distance Traveled Time elapsed Speed Distance Total traveled in Distance 1 second traveled 0 0 m s 0 0m 1 10 m s 5m 5m 2 20 m s 15 m 20 m 3 30 m s 25 m 45 m 4 40 m s 35 m 80 m Equations How fast Know distance and time use Know acceleration and time use How far Know velocity and time use Know acceleration and time use d v t v at v gt d vt 1 2 1 2 d at d gt 2 2 UNITS in Equations How fast Velocity d m v t s m m s m v at 2 s s s s 1 s How far acceleration m d vt s m s 2 1 2 1 m s d at 2 m 2 2 s 1 Problem Cat steps off ledge and reaches ground after second How fast was she going when she touched the ground What is the height of the ledge v gt 1 2 d gt 2 Cat s jump how fast 10m v 2 0 5s s 10m v 2 0 5s 5m s s Cat s jump how far 1 10m 2 d 2 0 5s 2 s 1 10m 2 d 2 0 5s 1 25m 2 s Acceleration of Gravity Gains speed for each interval of time that object is falling Acceleration of Gravity Loses speed for each interval of time it rises on an upward throw Gains at same rate on its downward path Hang time for basketball player Spud Webb slam dunk contest http www youtube com watch v BUu7drj9hPw He can jump 1 25 m How long is he in the air 1 2 d gt 2 2d t g 2d 2 1 25m t 0 5s 2 g 10m s to go up so double for time in the air
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