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)