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Ch1: 1D Kinematics 1. Preview of concepts 2. Recall main points: position, displacement, velocity and acceleration (geometrically and algebraically) 3. Discuss Pre-lecture and Check Points 4. Examples of problems 1. Preview Position x of point P in 1D: Axis, Origin, Direction Position, velocity, acceleration v 1. Preview Graphs x vs t, v vs t 2 Main Points Algebraic relationship from x to v to a. Start with x(t)=2t-1 2. Main Points Special case: Motion with constant a: from a to x Graphical x, v, a Algebraic x, v, a 3 Discuss Checkpoint 1:For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time? A B 1.2 Discuss CheckPoint 2: At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec? Set up problem (always same way ): 1. Picture: Axes with origin and direction 2. Equations relevant to problem and specified for axis choice 3. Constraint Equations 4. Solution 4. problems Previous page cont’d 4. problems Relative signs of x, v, a and relation to speed and slowing down or speeding up. Difference between the quantity and its magnitude. Given the axes we chose, and the origin we chose, is the quantity describing the motion (position or velocity or acceleration) A. A positive number B. A negative number C. Zero D. Not enough info is given to determine the number Example. Throw object up in the air. a. How high does it go above release point, given vo? 4. problems 1. 2. 3. 4. Picture with axes and origin Generic equations relevant for the problem Constraint equation Solution Example. Throw object up in the air. b. How long does it stay in the air, given vo? 4. problems 1. 2. 3. 4. Picture with axes and origin Generic equations relevant for the problem Constraint equation Solution 4. problems Example. Two objects up in the air. Released at same time, the first from h at v1o=0, the other from y=0 with v2o=vo At what time will they pass each other (similar to homework problem) 1.3 problems Example.