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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 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: • 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.
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.
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?
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?
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.
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.
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:
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?
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.
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?
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?
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?