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How To Go Nowhere Fast… Displacement, Velocity and Acceleration More Trig… Pythagorean Theorem r 2 x2 y 2 To find an angle, you need the inverse trig function i.e. x=y=1 What is r? ? Dynamics & Kinematics Dynamics is the study of motion and of physical concepts (i.e. relationship between force and mass) Kinematics is a part of dynamics description of motion Not concerned with the cause of the motion Quantities in Motion Any motion involves three concepts Displacement Velocity Acceleration These concepts can be used to study objects in motion Section 1.1: Displacement Defined as the change Displacement vs. Time graph in position d d f d i d f stands for final i stands for initial di df SI units are meters (m) Displacement vs. Distance Displacement is NOT the same as Distance i.e. Throw a ball straight up and then catch it at the same point you released it The distance is twice the height The displacement is zero Vector & Scalar Quantities Vector has magnitude & direction i.e. v - instantaneous velocity a - instantaneous acceleration Scalar has magnitude only (v, t, mass) Section 1.2: Speed Speed the total distance traveled divided by the total time elapsed d total vav ttotal Speed is a scalar quantity Average speed completely ignores any variations in the object’s actual motion Average Velocity… Velocity is the rate of change of displacement per unit time d d f d i vav t t f ti Slope is velocity!!! Units? [v ] m s Speed vs. Velocity Cars on both paths have the same average velocity… Why? … they have the same displacement (in the same time interval). The car on the blue path will have a greater average speed…Why? … the distance it travels is larger (in the same time interval)! Graphical Interpretation of Velocity Average velocity equals the slope of the line joining the initial and final positions (vs. time) x xB x A vav t t B t A A – start at 30m from start and decelerate (neg. acceleration) to B B – Velocity is 0 m/s Start to accelerate in reverse C – Constant velocity in reverse. D – At start position. Continue in reverse at constant velocity E – Begin to accelerate in forward direction (slow down in reverse). Stop at F. Position vs. Time Graphs What will the position vs. time graph look like for the following: 1. Stand still 2. Slow steady walk 3. Fast steady walk How should I move to reproduce the graph on the previous slide? Interactive Position Time Graph 1. Stand still 2. Slow steady walk 3. Fast steady walk 1-D Vector Problem Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip wins. a. Which boat wins and by how much? (Or is it a tie)? b. What is the average velocity of the winning boat? Section 2.4: Acceleration the rate of change in velocity per unit time (v/ t) v v f vi a t t f ti Units? [a ] m s2 Graphical Interpretation of Average Acceleration Average acceleration equals the slope of the line joining the initial and final velocities (vs. time) v v f vi a t t f ti Quick Quiz… Match each velocity vs. time graph to its corresponding acceleration vs. time graph. Section 2.4: Motion Diagrams (Relationship between a and v) Uniform velocity What is the acceleration? a=0 Relationship Between a and v v and a are in the same direction a is constant v is increasing Relationship Between a and v v and a are in opposite directions a is constant v is decreasing 1. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer. Red car – moves at a constant velocity Green Car – accelerates Blue Car - accelerates 2. Which car (red, green, or blue) experiences the greatest acceleration? Blue Car – Has the greatest acceleration Green Car – Has the 2nd greatest acceleration Red car – does not accelerate 3. Match the appropriate line to the particular color of car. Blue Car Green Car Red car Acceleration in Motion Animated Car Graphs d vs. t v vs. t a vs. t Positive Velocity, Positive Acceleration If you have positive velocity and positive acceleration you are going forward increasing your velocity. Positive Velocity, Negative Acceleration If you have positive velocity and negative acceleration you are going forward but slowing down Negative Velocity, Positive Acceleration If you have negative velocity and positive acceleration you are going backwards and slowing down in that direction. At some point you would start moving forward .... Negative Velocity, Negative Acceleration If you have negative velocity and negative acceleration you are going backwards and speeding up in that direction. Positive and Negative Velocity and Acceleration Velocity Acceleration Action Positive Positive Car is speed up in the forward direction Positive Negative Car is slowing down in the forward direction Negative Positive Car is slowing down in the reverse direction Negative Negative Car is speeding up in the reverse direction

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How To Go Nowhere Fast, Bigmouth strikes, Sinestro Corps, artist formerly known, BRAVE AND THE BOLD, MARVEL ADVENTURES AVENGERS, Kurt Anderson, fun comics, the Hulk, Robert Kowalewski

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posted: | 11/15/2008 |

language: | English |

pages: | 30 |

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