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Kinematics in One Dimension

CHAPTER 2. Kinematics in One Dimension. Pgs. 19-37. MECHANICS: the study of the motion of objects & related forces. Two divisions of mechanics:. Kinematics : describe HOW objects move Dynamics : deals with forces & WHY objects move. Translational Motion.

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Kinematics in One Dimension

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  1. CHAPTER 2 Kinematics in One Dimension Pgs. 19-37

  2. MECHANICS: the study of the motion of objects & related forces. Two divisions of mechanics: • Kinematics: describe HOW objects move • Dynamics: deals with forces & WHY objects move

  3. Translational Motion • In chapter 2, we will only discuss objects that move without rotating. • This type of motion is called: TRANSLATIONAL MOTION

  4. REFERENCE FRAME • Any measurement of position, distance, or speed must be made with respect to a frame ofreference.

  5. Reference frame or Frame of Reference • A person walks 5 km/h. The train is moving at 80 km/h with respect to the ground. How fast is the person going with respect to the ground?

  6. Specifying the Motion of an Object • We often specify the motion of an object by using a set of coordinate axes. This can represent our frame of reference. • For one dimensional motion, we choose the x-axis as the line along which motion takes place. • If an object is dropped, motion is vertical and we use the y-axis.

  7. DISTANCE vs. DISPLACEMENT • Distance traveled here is not the same as the DISPLACEMENT! • Displacement is the change in postion of the object or how far the object is from its starting position. Total distance traveled? 100 m Total displacement? 40 m

  8. Let’s say you go 50 m east. 50 m east 10 m south Then you go 10 m south You have gone a distance of 60 m, but your displacement is less than that! You could find it by using the Pythagorean Theorem. Where the displacement is equal to the hypoteneuse.

  9. Displacement is a vector. • Displacement has BOTH magnitude & direction. Vectors are represented with arrows. Displacement is represented with an X since it is along the x-axis. Displacement is then “the change in x” or x

  10. Positive Displacement • Change in displacement is • x = x2 – x1 = 30 m – 10 m = 20 m

  11. Negative Displacement • The person is walking in the opposite direction on the x-axis now • x = x2 – x1 = 10 m – 30 m = - 20 m The negative value here simply indicates a direction! (to the left)

  12. SPEED VS. VELOCITY • Speed is a SCALAR quantity. It is defined as the total distance traveled divided by the time it takes to travel this distance. • s = total distance/total time • Velocity is a VECTOR quantity. It is defined in terms of displacement rather than total distance.

  13. VELOCITY • AVG = TOTAL DISPLACEMENT VELOCITY TIME ELAPSED v = x t

  14. Velocity is a function of time • Top: car is traveling at a constant velocity. • Bottom: car is traveling with a varying velocity

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