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# Kinematics - The Study of Motion

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Describes displacement, velocity, acceleration as vectors and distance and speed as scalars, Show all needed equations and their use.
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### Kinematics - The Study of Motion

2. 2. Measuring Motion • The study kinematics requires the measurement of three properties of motion. • (1) displacement – the straight line distance between two points (a vector quantity) • (2) velocity – the change in displacement with respect to time (a vector quantity) • (3) acceleration – the change in velocity with respect to time (a vector quantity) • The term distance like displacement, refers to the change in position between two points, but not in a straight line. Distance is a scalar quantity. Speed refers to change in position with respect to time but unlike velocity, does not require straight line motion. Speed is a scalar quantity.
3. 3. Lake Tranquility A x x B Distance traveled from A to B Displacement from A to B Speed = Distance from A to B/ time Velocity = Displacement from A to B/ time
4. 4. VELOCITY & ACCELERATION • OBJECTS IN MOTION MAY MOVE AT CONSTANT VELOCITY (COVERING EQUAL DISPLACEMENTS IN EQUAL TIMES) OR BE ACCELERATED (COVER INCREASING OR DECREASING DISPLACEMENTS IN EQUAL TIMES). • VELOCITY MEASUREMENTS MAY BE OF TWO TYPES, AVERAGE VELOCITY (VELOCITY OVER A LARGE INTERVAL TIME) OR INSTANTANEOUS VELOCITY (VELOCITY OVER A VERY SHORT INTERVAL OF TIME). • ACCELERATION MAY BE UNIFORM OR NON UNIFORM. UNIFORM OR CONSTANT ACCELERATION REQUIRES THAT THE VELOCITY INCREASE OR DECREASE AT A CONSTANT RATE WHILE NON UNIFORM ACCELERATION DISPLAYS NO REGULAR PATTERN OF CHANGE.
5. 5. 1 sec 2 sec 3sec 4sec 5 sec EQUAL DISPLACEMENTS IN EQUAL TIMES 1 sec 2 sec 3sec 4sec REGULARLY INCREASING DISPLACEMENTS IN EQUAL TIMES CLICK HERE
6. 6. S D I S P L A C E M E N T time t S t S t POSITIVE ACCELERATION Equal time intervals result in increasingly larger displacements
7. 7. Average velocity between t1 and t2 Is the slope of the Secant line = S/ t D I S P L A C E M E N T time S t t1 t2 s1 s2 Secant line
8. 8. D I S P L A C E M E N T time s1 t1 Finding velocity at point t1, s1 (instantaneous velocity) Draw a tangent line at the point t S Find the slope of the tangent line Instantaneous velocity equals the slope of the tangent line
9. 9. DISPLACEMENT, VELOCITY & CONSTANT ACCELERATION • The velocity of an object at an instant can be found by determining the slope of a tangent line drawn at a point to a graph of displacement versus time for the object. • If several instantaneous velocities are found and plotted against time the graph of velocity versus time is a straight line if the object is experiencing constant acceleration. • The slope of the straight line velocity versus time graph is constant and since acceleration can be determined by the slope of a velocity – time graph, the acceleration is constant. • The graph acceleration versus time for a constant acceleration system is a horizontal line. (A slope of zero since constant acceleration means that acceleration is not changing with time!)
10. 10. D I S P L A C E M E N T Time V E L O C I T Y Time A C C E L E R A T I O N Time S t t v Slope of a tangent drawn to a point on a displacement vs time graph gives the instantaneous velocity at that point Slope of a tangent drawn to a point on a velocity vs time graph gives the instantaneous acceleration at that point PLOT OF INSTANTANEOUS VELOCITIES VS TIME
11. 11. MEASURING VELOCITY & ACCELERATION • VELOCITY IS MEASURED AS DISPLACEMENT PER TIME. UNIT FOR THE MEASUREMENT OF VELOCITY DEPEND ON THE SYSTEM USED. IN THE MKS SYSTEM (METERS, KILOGRAMS, SECONDS) IT IS DESCRIBED IN METERS PER SECOND. • IN THE CGS SYSTEM (CENTIMETERS, GRAMS, SECONDS - ALSO METRIC) IT IS MEASURED IN CENTIMETERS PER SECOND. • IN THE ENGLISH SYSTEM IT IS MEASURED AS FEET PER SECOND. • ACCELERATION IN THE MKS SYSTEM IS EXPRESSED AS METERS PER SECOND PER SECOND OR METERS PER SECOND SQUARED. • IN CGS UNITS IT IS CENTIMETERS PER SECOND PER SECOND OR CENTIMETERS PER SECOND SQUARED. IN THE ENGLISH SYSTEM FEET PER SECOND PER SECOND OR FEET PER SECOND SQUARED ARE USED.
12. 12. GRAVITY & CONSTANT ACCELERATION • Gravity is the most common constant acceleration system on earth. As object fall under the influence of gravity (free fall) they continually increase in velocity until a terminal velocity is reached. • Terminal velocity refers to the limiting velocity caused by air resistance. In an airless environment the acceleration provided by gravity would allow a falling object to increase in velocity without limit until the object landed. • In most problems in basic physics air resistance is ignored. In actuality, terminal velocity is related to air density, surface area, the velocity of the object and the aerodynamics of the object (the drag coefficient).