Frame of Reference A coordinate frame is required in order to describe motion. The motion of an object is described relative to this coordinate frame of reference. In this course our frame of reference will be the Cartesian Coordinate System. Arrrrg!! Me palm tree….Matey! Positive and Negative Displacement Depends on your frame of reference. Convention is: Moving right is positive, +x, 0°, East Moving left is negative, -x, 180°, West Moving up is positive, +y, 90°, North Moving down is negative, -y, 270°, South Velocity Kinematics - The branch of mechanics that studies bodies undergoing change of position (displacement). Velocity-The rate of change of an object’s position. Scalar-a quantity with magnitude but no direction. – Vector- a quantity with magnitude and direction. – Examples: mass, temperature, energy, speed, distance Examples: displacement, velocity, force, acceleration 5 miles – vector or scalar? 5 miles, north –vector or scalar? 45o C – vector or scalar? 28.34 g ? 12 N (Newtons) at 045o ? 320 birds ? East ? 5 miles, west ? 300 J (joules) 45 miles per hour ? 2.54 cm ? Distance and Displacement Distance is a scalar quantity – How much ground an object has covered. Displacement is a vector quantity – Change in position, from the origin in the frame of reference. Question????? What is the distance of cars in the INDY 500? What is displacement of cars in the INDY 500? Use problem solving techniques to solve this problem A cross country skier goes in the positive X direction 180 meters for one minute He reverses direction(-) and goes 140 meters for another minute. He reverses again (+) and goes 100 meters for another minute. What is his distance? What is his displacement? (remember to express direction) Speed and Velocity Speed is a scalar quantity Velocity is a vector quantity. The direction of the velocity vector is the same as the change of displacement vector. Velocity = change in position/time velocity = displacement/time Speed = distance/time From the previous skier problem, what is the skiers speed? What is the skier’s velocity? The wander’s journal Average and Constant Velocity Average velocity is the change in position (displacement) divided by the time interval over which the change occurred. Vavg = ∆d/ ∆t = (df – di)/(tf – ti) = rise / run If the average velocity of an object does not change, then the object is moving at constant velocity. Constant velocity is also called uniform velocity. Average and Constant Velocity IF…and ONLY IF….the velocity changes uniformly, we can also calculate average velocity with: Vf Vi V avg 2 Instantaneous Velocity Instantaneous velocity is the average velocity over a very tiny interval of time (approaching zero seconds). Graphically, it is the slope of the tangent to a position-time graph at a point. Picturing Motion:Position Time Graphs A Displacement Time Graph (d-t graph) describes the motion of an object by showing the change in position in relation to time. The slope of the position time is the velocity of the object. Speed & Velocity Average, Instantaneous, Constant 1. Describe the motion of each car. 2. Give the velocity of car A at a. b. c. t=3s t=5s t = 10 s 3. Car B at: a. b. t=7s the interval between t = 0 and t = 10 sec 4. Car C at: a. b. c. t=7s t=9s the interval between t = 0 and t = 10 sec 5. Give the velocity of Car D at: a. the interval between t = 0 and t = 10 sec 6. Car E at: a. the interval between t = 0 and t = 8 sec b. the interval between t = 8 and t = 10 sec c. the interval between t = 0 and t = 10 sec Calculating Displacement from Average Velocity The average velocity equation can be rearranged to calculate displacement Vavg = ∆d/ ∆t Vavg(∆t) = ∆d If velocity changes at an even (uniform) rate, we can still use this equation by substituting average velocity for Vavg Vf Vi (t ) d 2 Problems Example Problems, page 61 #17, #18, #20