UNIT 2 CVM INSTANTANEOUS VELOCITY AND GRAPHICAL REPRESENTATIONS OF POSITON VS. TIME OBJECTIVES I CAN IDENTIFY AN OBJECTS DIRECTION OF MOTION, INITIAL POSITION, AND RELATIVE SPEED FROM A POSITION VS. TIME GRAPH SOLVE FOR TIME, VELOCITY, OR DISTANCE IN PROBLEMS USING THE CONSTANT VELOCITY EQUATION DRAW 2 GRAPHICAL REPRESENTATIONS OF AN OBJECTS POSITION VS. TIME. Position vs. Time Position (m) Time (s) t x WHEN WE LAST LEFT OFF Instantaneous Velocity (or simply velocity) -This refers to the specific velocity at specific time -As opposed to an average velocity -Units (m/s) MY APOLOGIES! SYMBOL CORRECTIONS SYMBOLPRONOUNCIATIONMEANING x i x 0 X nautInitial x-position x f x XFinal x-position t TTime (as a variable, any time measurement) t i t 0 T nautInitial time (starting time) t f t T finalFinal time (same as just t) Y = M X + B X = V T + X 0 Y = M X + B X = V T + X 0 If V is constant, than it is equivalent to V 0, so the equation becomes: Y = M X + B X = V T + X 0 Constant Velocity Equation or If V is constant, than it is equivalent to V 0, so the equation becomes: QUICK NOTE: SPEED SPEED IS VELOCITY WITHOUT A DIRECTION I.E. 30M/S AS OPPOSED TO 30M/S NORTH THIS MAKES SPEED A SCALAR AND VELOCITY A VECTOR SPEED IS ALSO THE MAGNITUDE OR ABSOLUTE VALUE OF VELOCITY Position (m) Time (s) A B -What can you say about As -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? Position (m) Time (s) A B -What can you say about As -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? -What can you say about Bs -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? Position (m) Time (s) A B -What can you say about As -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? -What can you say about Bs -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? -Which one has a greater velocity? -How do you know? Position (m) Time (s) A B -What can you say about As -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? Position (m) Time (s) A B -What can you say about As -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? -What can you say about Bs -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? Position (m) Time (s) A B -What can you say about As -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? -What can you say about Bs -Direction of motion? +/-? -Initial Position? +/-/0? -Velocity? +/-? -Which one has a greater SPEED? -How do you know? CONSTANT VELOCITY PROBLEMS 1.Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in: s? s? CONSTANT VELOCITY PROBLEMS 1.Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in: s? s? 2.The distance between home and first is 26.82m (88ft). How long would it take him to reach first base? CONSTANT VELOCITY PROBLEMS 1.Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in: s? s? 2.The distance between home and first is 26.82m (88ft). How long would it take him to reach first base? 3.The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in It was recorded going 173.3km/h. 1.How fast was this in m/s? CONSTANT VELOCITY PROBLEMS 1.Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in: s? s? 2.The distance between home and first is 26.82m (88ft). How long would it take him to reach first base? 3.The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in It was recorded going 173.3km/h. 1.How fast was this in m/s? 2.It is 18.39m from the pitchers mound to home plate. How long did it take Aroldis pitch to reach home plate? CONSTANT VELOCITY PROBLEMS 1.Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in: s? s? 2.The distance between home and first is 26.82m (88ft). How long would it take him to reach first base? 3.The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in It was recorded going 173.3km/h. 1.How fast was this in m/s? 2.It is 18.39m from the pitchers mound to home plate. How long did it take Aroldis pitch to reach home plate? 4.Aroldis windup takes 2.35s and Ichiro is trying to steal home. Can he make it? (it is the same distance from 3 rd base to home as it is from home base to 3 rd ) CONSTANT VELOCITY PROBLEMS 1.Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in: s? s? 2.The distance between home and first is 26.82m (88ft). How long would it take him to reach first base? 3.The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in It was recorded going 173.3km/h. 1.How fast was this in m/s? 2.It is 18.39m from the pitchers mound to home plate. How long did it take Aroldis pitch to reach home plate? 4.Aroldis windup takes 2.35s and Ichiro is trying to steal home. Can he make it? (it is the same distance from 3 rd base to home as it is from home base to 3 rd ) 1.If Ichiro cheats out by 2.50m, can he make it? GRAPHICAL REPRESENTATIONS OF POSITION VS. TIME MOTION GRAPHS A MOTION MAP REPRESENTS THE POSITION, VELOCITY, AND ACCELERATION OF AN OBJECT AT VARIOUS CLOCK READINGS. (AT THIS STAGE OF THE CLASS, WE WILL BE REPRESENTING POSITION AND VELOCITY ONLY.) SUPPOSE THAT YOU TOOK A STROBOSCOPIC PICTURE OF A CAR MOVING TO THE RIGHT AT CONSTANT VELOCITY WHERE EACH IMAGE REVEALED THE POSITION OF THE CAR AT ONE- SECOND INTERVALS. THIS IS THE MOTION MAP THAT REPRESENTS THE CAR. WE MODEL THE POSITION OF THE OBJECT WITH A SMALL POINT. AT EACH POSITION, THE OBJECT'S VELOCITY IS REPRESENTED BY A VECTOR. IF THE CAR WERE TRAVELING AT GREATER VELOCITY, THE STROBE PHOTO MIGHT LOOK LIKE THIS: NOTE THE DIFFERENCES BETWEEN THE CAR TRAVELING FASTER AND THE ONE TRAVELING SLOWER IF THE CAR WERE MOVING TO THE LEFT AT CONSTANT VELOCITY, THE PHOTO AND MOTION MAP MIGHT LOOK LIKE THIS: MORE COMPLICATED MOTION CAN BE REPRESENTED AS WELL. HOW WOULD YOU DESCRIBE THE MOTION OF THE OBJECT HERE? MORE COMPLICATED MOTION CAN BE REPRESENTED AS WELL. HOW WOULD YOU DESCRIBE THE MOTION OF THE OBJECT HERE? HERE, AN OBJECT MOVES TO THE RIGHT AT CONSTANT VELOCITY, STOPS AND REMAINS IN PLACE FOR TWO SECONDS, THEN MOVES TO THE LEFT AT A SLOWER CONSTANT VELOCITY. HOMEWORK DUE 8/25 READ AND COMMENT ON 2 OF YOUR CLASSMATES BLOGS PLEASE MAKE THE COMMENTS MEANINGFUL!