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Kinematics

Kinematics. The science of describing the motion of objects utilizing words, diagrams, numbers, graphs, and equations; branch of mechanics (study of motion of objects). Language of Kinematics:.

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Kinematics

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  1. Kinematics The science of describing the motion of objects utilizing words, diagrams, numbers, graphs, and equations; branch of mechanics (study of motion of objects).

  2. Language of Kinematics: • The mathematical quantities utilized to describe motion of objects can be divided into two categories: • 1. Scalars-quantities described by magnitude (numerically) only. • 2. Vectors-quantities described by magnitude and direction.

  3. One dimensional motion… • The simplest type of motion. • Motion takes place over time and depends upon the frame of reference. • Frame of reference-a system for specifying the precise location of objects in space and time.

  4. Distance and displacement: • Distance-a scalar quantity; how far something travels. • Displacement-a vector quantity, change in position (how far an object travels in a given direction). • How are distance and displacement unique?

  5. Sample Situation: • A physics teacher walks 4m East, 2m South, 4m West, and finally 2m North. Depict the situation. • What is the total distance? • What is her displacement? • Is she out of place?

  6. Speed and velocity: • Speed-denotes how fast an object moves; rate at which distance is covered; scalar. • Velocity-how fast something moves in a given direction; vector.

  7. Describing motion with diagrams: • Ticker tape diagram-situation where a long tape is attached to a moving object and threaded to a device that places a tick upon the tape at regular intervals. As the object moves, the tape is dragged through the ticker leaving a trail of dots to represent the history of the motion. • Vector diagram-depict the direction and relative magnitude of a vector quantity by a vector arrow.

  8. Vf = Vi + at ∆X= Vit + 1/2at2 vf2 = vi2 + 2a(∆X) ∆X= 1/2(vf)t ; Vf=a∆t; ∆X=1/2a(∆t)2; vf2=2a∆X (when accelerating object starts from rest) Kinematic Equations:

  9. Average Velocity and Displacement and Average Acceleration: • Sample Problem A: • During a race on level ground, Andra runs with an average velocity of 6.02m/s to the east. What is Andra’s displacement after 137s? Sample Problem B: A shuttle bus slows down with an average acceleration of -1.8m/s2. How long does it take the bus to slow from 9.0m/s to a complete stop?

  10. Displacement with constant acceleration: • Sample Problem C: • A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find the distance that the car travels duirng braking.

  11. Velocity and Displacement with Constant Acceleration: • Sample Problem D: • A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

  12. Final Velocity After Any Displacement: • Sample Problem E: • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500m/s2. What is the velocity of the stroller after it has traveled 4.75m?

  13. Falling Object: • Sample Problem F: • Jason hits a volleyball so that it moves with an initial velocity of 6.0m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor?

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