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SJSU PHYS 2A - Motion in One Dimension

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Chapter 2Motion in One DimensionDynamics The branch of physics involving the motion of an object and the relationship between that motion and other physics concepts Kinematics is a part of dynamics In kinematics, you are interested in the description of motion Not concerned with the cause of the motionQuantities in Motion Any motion involves three concepts Displacement Velocity Acceleration These concepts can be used to study objects in motionBrief History of Motion Sumaria and Egypt Mainly motion of heavenly bodies Greeks Also to understand the motion of heavenly bodies Systematic and detailed studies Geocentric model“Modern” Ideas of Motion Copernicus Developed the heliocentric system Galileo Made astronomical observations with a telescope Experimental evidence for description of motion Quantitative study of motionPosition Defined in terms of a frame of reference A choice of coordinate axes  Defines a starting point for measuring the motion Or any other quantity One dimensional, so generally the x-or y-axisDisplacement Defined as the change in position f stands for final and i stands for initial Units are meters (m) in SIf ix x x∆ ≡ −Displacement Examples From A to B xi= 30 m xf= 52 m ∆x = 22 m The displacement is positive, indicating the motion was in the positive x direction From C to F xi= 38 m xf= -53 m ∆x = -91 m The displacement is negative, indicating the motion was in the negative x directionDisplacement, GraphicalVector and Scalar Quantities Vector quantities need both magnitude (size) and direction to completely describe them Generally denoted by boldfaced type and an arrow over the letter + or – sign is sufficient for this chapter Scalar quantities are completely described by magnitude onlyDisplacement Isn’t Distance The displacement of an object is not the same as the distance it travels Example: Throw a ball straight up and then catch it at the same point you released it The distance is twice the height The displacement is zeroSpeed The average speed of an object is defined as the total distance traveled divided by the total time elapsed Speed is a scalar quantity==total distanceAverage speedtotal timedvtSpeed, cont Average speed totally ignores any variations in the object’s actual motion during the trip The total distance and the total time are all that is important Both will be positive, so speed will be positive SI units are m/sVelocity It takes time for an object to undergo a displacement The average velocity is rate at which the displacement occurs Velocity can be positive or negative ∆t is always positive−∆= =∆ −f iaveragef ix xxvt t tVelocity continued Direction will be the same as the direction of the displacement, + or - is sufficient Units of velocity are m/s (SI) Other units may be given in a problem, but generally will need to be converted to these In other systems: US Customary: ft/s cgs: cm/sSpeed vs. Velocity Cars on both paths have the same average velocity since they had the same displacement in the same time interval The car on the blue path will have a greater average speed since the distance it traveled is largerGraphical Interpretation of Velocity Velocity can be determined from a position-time graph Average velocity equals the slope of the line joining the initial and final positions An object moving with a constant velocity will have a graph that is a straight lineAverage Velocity, Constant The straight line indicates constant velocity The slope of the line is the value of the average velocityNotes on Slopes The general equation for the slope of any line is The meaning of a specific slope will depend on the physical data being graphed Slope carries unitschange in vertical axisslopechange in horizontal axis=Average Velocity, Non Constant The motion is non-constant velocity The average velocity is the slope of the straight line joining the initial and final pointsInstantaneous Velocity The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The instantaneous velocity indicates what is happening at every point of time∆ →∆≡∆lim0txvtInstantaneous Velocity on a Graph The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous velocity at that time The instantaneous speed is defined as the magnitude of the instantaneous velocityAcceleration Changing velocity means an acceleration is present Acceleration is the rate of change of the velocity Units are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust) −∆= =∆ −f if iv vvat t tAverage Acceleration Vector quantity When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasingNegative Acceleration A negative acceleration does not necessarily mean the object is slowing down If the acceleration and velocity are both negative, the object is speeding upInstantaneous and Uniform Acceleration The limit of the average acceleration as the time interval goes to zero When the instantaneous accelerations are always the same, the acceleration will be uniform The instantaneous accelerations will all be equal to the average accelerationGraphical Interpretation of Acceleration Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graphAverage AccelerationRelationship Between Acceleration and Velocity Uniform velocity (shown by red arrows maintaining the same size) Acceleration equals zeroRelationship Between Velocity and Acceleration Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing (red arrows are getting longer) Positive velocity and positive accelerationRelationship Between Velocity and Acceleration Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting


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