Kinematics Big Ideas and Equations Position vs. Time graphs Big Ideas: A straight line on a p vs t graph indicates constant speed (and velocity) An object at rest is indicated by a horizontal line The slope of a line on a p vs. t graph = velocity of the object (steeper = faster) The main difference between speed and velocity is that velocity incorporates direction o Speed will always be positive but velocity can be positive or negative o Positive vs. Negative slopes indicates the direction; toward the positive end of an axis (number line) or the negative end. For motion detectors this indicates toward (-) and away (+), but only because there is no negative side to the axis. An object with continuously changing speed will have a curved P vs. t graph; (curving steeper – speeding up, curving flatter – slowing down) (Instantaneous) velocity = average velocity if P vs. t is a (straight) line. Velocity vs Time graphs Big Ideas: The velocity can be found by calculating the slope of a position-time graph Constant velocity on a velocity vs. time graph is indicated with a horizontal line. Changing velocity is indicated by a line that slopes up or down. Speed increases when Velocity graph slopes away from v=0 axis. Speed decreases when velocity graph slopes toward v=0 axis. The velocity is negative if the object is moving toward the negative end of the axis - if the final position is less than the initial position (or for motion detectors if the object moves toward the detector) The slope of a velocity vs. time graph = the acceleration of the object Equations: Speed = Absolute value of velocity Average Speed = Total Distance traveled (Direction does not matter) Total Time Average Velocity = Final Position - Initial Position Total Time Velocity = Average Velocity IF velocity is constant (P vs t is straight line) Acceleration = v Units are distance units per unit of time squared (i.e. m/s2) t Graphs: Look at the slope of one graph to determine what the next graph (to the right) will look like. An object moving at constant velocity away from the origin: Slope is constant Slope = 0 Acceleration = 0 and positive V is positive An object is moving at constant velocity in the negative direction toward the origin: Slope is constant Slope = 0 Acceleration = 0 and negative V is negative An object speeding up away from the origin in positive direction: Slope is increasing in Slope is constant Acceleration is constant positive direction and positive and positive V is positive An object speeding up towards the origin in negative direction: Slope is increasing in Slope is constant Acceleration is constant negative direction and negative and negative V is negative An object slowing down away from the origin in the positive direction: Slope is decreasing Slope is constant Acceleration is constant In positive direction and negative and negative V is positive An object slowing down while moving toward the origin in the negative direction: Slope is negative, Slope is constant Acceleration is constant decreasing and positive V negative Strobe Pictures (Motion Diagrams): Another way to represent motion Gives position information, but not time information Time information can be determined with the flash interval (time interval between images) Strobe diagrams can be created through placing a dot on a position line (ruler) each time the strobe flashes (i.e. one dot for each second if the time interval is one second) 0 50 100 150 200 250 pos. (m) .