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Kinematics Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Describing Motion with Position vs. Time Graphs. Ex:car moving with a constant, rightward (+) velocity of 10 m/s. What would a graph for this motion look like?.

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## Describing Motion with Position vs. Time Graphs

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**KinematicsKinematics is the science of describing the motion**of objects using words, diagrams, numbers, graphs, and equations.**Describing Motion with Position vs. Time Graphs**Ex:car moving with a constant, rightward (+) velocity of 10 m/s. What would a graph for this motion look like?**Determining Velocity on a p vs.t Graph**• The slope of a position-time graph is the average velocity!!!!!!!!!!! • Pick two points on the line and determine their coordinates. • Determine the difference in y-coordinates of these two points (rise). • Determine the difference in x-coordinates of these two points (run). • Divide the difference in y-coordinates (rise) by the difference in x-coordinates (run).**25m-5m =20m =4m/s**5s - 0s 5 s**What can you say about the motion of the two objects**represented in these graphs? Fast, moving right (+) Constant Velocity Slow, moving right (+) Constant Velocity**What can you say about the motion of the two objects**represented in the graphs? Slow, moving left (–) Constant Velocity Fast, moving left (–) Constant Velocity**What if the object does not travel at a constant velocity?**• Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity • The shape of a position vs. time graph can tell you what kind of motion is occurring: • Straight line = constant velocity • Curved line = changing velocity= acceleration**Ex. 2 A car that is moving rightward and speeding up or**accelerating in + direction. What would its graph look like?**Note that the constant velocity object has a constant slope**and the accelerating object has a non-constant slope.**The Direction of the Acceleration Vector**• Since acceleration is a vector quantity, it has a direction associated with it. The direction of the acceleration vector depends on two things: • whether the object is speeding up or slowing down • whether the object is moving in the + or - direction**The general RULE OF THUMB is:**• If an object is slowing down, then its acceleration is in the opposite direction of its motion.**Slow to fast, moving right (+), acceleration in +**direction Fast to slow, moving right (+) deceleration= negative acc.**Moving left (–) Velocity; Slow to Fast,**Acceleration (-) Leftward (-) Velocity; Fast to Slow Acceleration (+)**Velocity vs. time graphs**velocity velocity**Some practice with graph shapes**• 1. Sketch a position-time graph for an object which is moving with a constant, positive velocity. • 2. Sketch a position-time graph for an object which is moving with a constant, negative velocity. • 3. Sketch a position-time graph for an object moving in the + dir'n and accelerating from a low velocity to a high velocity. • 4. Sketch a position-time graph for an object moving in the + dir'n and accelerating from a high velocity to a low velocity. • 5. Sketch a position-time graph for an object moving in the - dir'n and accelerating from a high velocity to a low velocity. • 6. Sketch a position-time graph for an object moving in the - dir'n and accelerating from a low velocity to a high velocity.**7. Sketch a position-time graph for an object moving in the**+ dir'n with constant speed; first a slow constant speed and then a fast constant speed. • 8. Sketch a position-time graph for an object moving in the + dir'n with constant speed; first a fast constant speed and then a slow constant speed. • 9. Sketch a position-time graph for an object moving in the - dir'n with constant speed; first a slow constant speed and then a fast constant speed. • 10. Sketch a position-time graph for an object moving in the - dir'n with constant speed; first a fast constant speed and then a slow constant speed. • 11. Sketch a position-time graph for an object which moves in the + direction at a slow constant speed and then in a - direction at a fast constant speed. • 12. Sketch a position-time graph for an object which moves in the + direction at a fast constant speed and then in a - direction at a slow constant speed. • 13. Sketch a position-time graph for an object which moves in the - direction at a slow constant speed and then in a + direction at a fast constant speed.

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