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KINEMATICS

Learn about the concepts of position, distance, and velocity in kinematics, including key terms such as displacement, instantaneous velocity, and acceleration. Explore graphs and formulas to understand motion better.

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KINEMATICS

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  1. KINEMATICS KONICHEK

  2. I. Position and distance • A. Position- The separation between an object and a reference point • 1. To locate something we must make some point a zero point- reference point • 2. Measures both distance and direction • B. Distance- needs no reference. • 1. Measures the amount of separation • 2. Measurement of only length • C. Time- this is the interval between on reading of separation to the next reading of separation

  3. D. Speed( rate)= displacement/ time • 1. Units of distance/ unit of time • 2. Instantaneous speed- the speed of the object at the time of the observation. • a. Looking at ones speedometer. • 3. Average speed= total distance/total time • a.SA= DT/TT

  4. E. Scalar and vector quantities. • 1. Scalar-measures only the magnitude or size • a. Distance • b. Speed is a scalar- tells only how fast • 2. Vector- measures magnitude and direction

  5. II. Velocity • A. Velocity- Speed in a given direction… • 1.vector • B. Constant velocity- • 1. Motion remains constant at the same speed

  6. C. Changing velocity- constant velocity and constant speed are not the same • 1. Constant speed can happen even if direction is changing • 2. Constant velocity cannot occur- changing direction • D. Instantaneous velocity- this is the position of a moving object • 1. The position of the object changes with each new time taken.

  7. E. Displacement-The change of position of an object. • 1. Final distance - initial distance= ΔD • F. Time for moving objects • 1. Final time - initial time=ΔT

  8. D. Average velocity is the ratio of the change in displacement to a change in time • 1. Va= d2-d1/t2-t1 • E. Constant velocity- Occurs when the average velocity is the same for all time intervals • 1. Also called uniform velocity: • Δd/Δ t is constant. • a. The equation then comes to v=d/t. This represents uniform velocity.

  9. F. Position-time graphs. • 1. Shows the position as a function of time • 1. Time on X-axis, position on X- axis • 2. Slope of a position- time graph. • a. The ratio of displacement to time is the same as rise over run of the line (slope)

  10. III. POSITIVE AND NEGATIVE VELOCITIES. • A. Displacement can occur either positive or negative • 1. Positive moves to the right of the reference point • 2. Negative- moves to the left of the reference point

  11. B. Time is always positive • C. Speed is the magnitude of the velocity • D. Velocity- includes speed and direction of a moving object • 1. Can have a positive or negative velocity • a. Depends which way the object is moving relative to the frame of reference.

  12. IV. Instantaneous velocity- The finding of the velocity for an instant. • A. Like looking at the speedometer of your car for just an instant. • B. It’s the slope of the tangent- If the graph shows an increasing velocity over various times the line is not a straight line, so the slope gives the instantaneous velocity. • 1. First derivative of the displacement formula or limit ΔX/ΔT

  13. V. Velocity-Time graph- very useful tool to describe motion. • A. time- x-axis, velocity on the y-axis • B. The area under the line is equal to the displacement of the object from its original position • 1. When velocity is constant displacement increases linearly with time • a. Line is straight

  14. VI Motion • A. Speed- How fast an object is moving relative to a reference frame • 1. ratio between distance and time ( scalar quantity-tells how fast) • a. speed=distance/time( S=d/t) • b. m/s, Km/hr, Mi/hr • 2. constant speed- when an equal distance is covered over an equal time • 3, Graphing speed • a. time is on X axis • b. distance on the Y axis • c. the speed of the car can be calculated by calculating the slope of the line( rise/ run).. Y=mx+b • 1, steeper the slope faster it’s going

  15. Graphing of Velocity • Low velocity High velocity

  16. VII. Relative velocity- this is the velocity as seen from a stationary frame of reference • A. A boat is traveling at 8m/s and a man on the boat is walking at 2m/s a man observing from the shore would see the man walking at 10m/s

  17. I. Acceleration- vector quantity • A. The rate which an objects velocity changes • 1. Has to do with changing how fast is moving. • 2. Acceleration occurs when an object changes its velocity with respect to time.

  18. B. Constant velocity-When an object changes its velocity by the same amount each second. • 1. Not the same as a constant velocity • 2. The velocity is changing the same amount for every increment of time • a. constant velocity is not accelerating • 3. Since accelerating objects are constantly changing their velocities- The distance traveled per unit time is not a constant. • a. Free falling objects accelerate- objects in free fall will cover a longer distance over each period of time it has fallen

  19. C. LAW- FOR OBJECTS WITH A CONSTANT ACCELERATION, THE DISTANCE OF TRAVEL IS DIRECTLY PROPORTIONAL TO THE SQUARE OF THE TIME TRVALED. • 1. Object travels twice the time it will go 4 times the distance. • 2. travels 3 times the time, distance is 9 times father.

  20. II. Calculating acceleration. • A. Ave acceleration= change in velocity/ time ave accel= Vf- Vi/t or ΔV/T • 1. units- m/s2 cm/s2 ft/s2 • B. Acceleration is a vector- has a direction • 1. Depends if it is speeding up or slowing down. • 2. moving in a positive or negative direction

  21. C. Rule of thumb • 1. If the object is slowing down, then the acceleration is in the opposite direction of motion. • 2.can determine if the sign is positive or negative., right or left, up or down. • a. speeding up- accel is in the same direction as the velocity so it’s positive • b. slowing down- acceleration is opposite that of the velocity, so it’s negative • 3. direction- when the velocity is increasing in the direction of the speed- positive accel • 4. When an object is slowing down in the direction of the velocity- negative accel

  22. I. Acceleration-A change in velocity • A. A change in speed or direction may occur • 1. a= ΔV/ΔT • a. change in velocity/ change in time • 2. values may be positive or negative • a. positive speeding up • b. negative slowing down

  23. II.Velocity of an object with constant acceleration • A. Constant acceleration ( uniform) • 1. accel doesn’t change with time • a. Vf= Vi +at

  24. III. Displacement during constant acceleration • A. object is moving at a constant velocity • 1. The area under a velocity time graph • B. d= ½(Vf+ Vi)t

  25. IV Displacement when acceleration and time are known • A. combine the velocity with constant acceleration and the displacement during constant acceleration • 1. d= ½(Vf+ Vi)T-1/2(Vi+aT)+ Vi-1/2((2Vi+aT)t-- • a. d= ViT+1/2at2 • a. ViT= displacement moving at a constant velocity • b. 1/2at2= displacement from rest to and moving with uniform acceleration • c. the sum of the 2 terms gives the displacement of an object that starts with an initial velocity and accelerates uniformly. • 2. starting from rest the equation comes down to d=1/2at2

  26. B. Velocity-time graph of uniform acceleration- the area under the curve equals the displacement. • C. The curve for an accelerating position-time graph is parabolic • 1. When one value increases the other varies as the square of it. • a. Y= X • D. The slope of a position-time graph of an accelerating is a tangent point to the parabolic function • 1. Calculus people- second derivative function of the displacement formula

  27. V. Displacement when velocity and acceleration are known. • A. combine the final velocity and displacement • 1. d=1/2(Vf-Vi)t and Vf= Vi+at, solve for t and substitute in the first equation • a. final equation V2f= V2i +2ad

  28. VI acceleration due to gravity • A. Galileo- first to show objects fall to the earth with the same acceleration. • 1. Rolled balls down an incline plane which rang bells at intervals • B. acceleration of gravity is represented byg • 1. The acceleration is -9.8m/s2 • a. vector- designate up as positive, and down as negative • b. for each second something drops its speed increases by 9.8m/s • 2. equations for acceleration of gravity • a.Vf=Vi +gt • b. V2f= V2i+ 2gd • c. d= Vi+1/2 gt2

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