Linear and Non Linear Motion Reading Supplemental Textbook Materials pages 273 287 Acceleration Rate of increase of a rate d t t Increases rate for each increment in time that has passed So there is an increased of 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 1 2 d vt d gt Average velocity 2 Va Vi Vf 2 d vi vf 2 t v at or v gt Substitute this v into d vt d vi vf 2 t with vi 0 1 2 d gt 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 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 Equations How fast How far 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 25s 1 25m 2 s Basketball Player Hangtime Spud Webb had 1 25 m vertical jump How long could he stay in the air 2d 10m t g 2 g s 1 2 d gt 2 2 1 25m t 0 5s 10m 2 s Acceleration Rate of increase of a rate d t t Increases rate for each increment in time that has passed So there is an increased of distance for each successive time interval Relative Motion With respect to another object Earth moving 30 km s Airplane has airspeed There is windspeed Influences groundspeed Relative Motion Airplane flies 100 mi h Wind blowing 20 mi h Same direction simple adding Opposite direction subtract Differing directions draw to scale or solve Diagonal speeds Vector has magnitude and direction Resultant Vector Add the two Same direction simple adding Opposite direction subtract Differing directions draw to scale or solve Solving Diagonal Vectors Use Pythagorean theorem a2 b2 c2 works for lengths of legs of right triangles c a b Diagonal Vectors Draw rectangle of components a and b Draw diagonal of rectangle Legs on right angle are a and b Diagonal is c c a b Diagonal Vectors Boat traveling 8 km h b Crossing river flowing 6 km h a What is boat s speed across river c a b c Diagonal Vectors Boat traveling 8 km h b2 64 Crossing river flowing 6 km h a2 36 What is boat s speed across river c 36 64 100 10km h c a b Types of Motion Linear in a straight line Non linear curved path Projectiles have curved path called parabola Parabolic curves are parabolas Projectiles Move both horizontally and vertically Vertical motion influenced by gravity Horizontal motion not influenced by gravity Are NOT dependent upon one another Roll the Ball Freely falling object Has acceleration downward Pushed away from table Has velocity outward Combines to have a parabolic path Path of Ball from Side Ball Rolling off table vertical horizontal Top View of the ball Top View Series2 distance from table Front View the ball Front View Projectile motion Each component acts separately Same horizontal distance in each time increment Vertical distance increases for each time increment that passes Path of Ball from Side Ball Rolling off table vertical horizontal What if What if you were at a level shooting range and dropped a bullet from your hand at exactly the instant a shooter fired a bullet at a paper target 1000 meters away Which bullet would hit the ground first Cannon Ball Trajectory with no Gravity 350 300 Vertical height 250 200 150 100 50 0 0 50 100 150 200 250 Horizontal distance 300 350 Cannonball with Gravity 90 80 V ertical H eig h t 70 60 50 40 30 20 10 0 0 10 20 30 40 50 Horizontal Distance 60 70 80 90 Faster Cannonball 350 300 H eig h t 250 200 150 100 50 0 0 50 100 150 200 Distance 250 300 350 How Fast is it going Horizontal Speed does not change Vertical speed function of time How fast was it going up to begin with This changes due to acceleration of gravity v0 v gt v0 vchange Steeper Cannonball 350 300 Vertical 250 200 150 100 50 0 0 50 100 150 200 Horizontal 250 300 350 Acceleration of Cannonball Cannonball What is the acceleration in a horizontal direction 90 80 70 V e r tic a l 60 50 40 30 20 10 0 0 10 20 30 40 50 Horizontal 60 70 80 90 Acceleration of Cannonball Cannonball What is the acceleration in a vertical direction 90 80 70 V e r tic a l 60 50 40 30 20 10 0 0 10 20 30 40 50 Horizontal 60 70 80 90 Cannonball Trajectories Cannonball trajectories Projectile will fall from maximum height in same amount of time it took to rise Because the acceleration of gravity slows it at the same rate it increases the speed on the way down
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