ppt_chapter02.ppt - Raymond A Serway John W Jewett Chapter 2 Motion in One Dimension The Study of Motion • • Kinematics describes motion while

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Raymond A. Serway John W. Jewett Chapter 2 Motion in One Dimension
The Study of Motion Kinematics describes motion while ignoring the agents that caused the motion For now, we will consider motion in one dimension Along a straight line We will use the particle model A particle is a point-like object, has mass but infinitesimal size
2.1 Average Velocity Average speed is defined as Speed is not a vector, so has no direction Average velocity is a vector quantity
2.1 Average Velocity The motion of a particle can be specified if its position is known at all times Consider the car moving back and forth along the x axis The figure is a pictorial representation of the motion Imagine we take data on the position of the car every 10 s
2.1 Average Velocity The graphical representation of the motion is a position-time graph The smooth curve is a guess as to what happened between the data points
2.1 Average Velocity The tabular representation of the motion is shown here The data are entries for position at each time
2.1 Average Velocity Average velocity : defined as ratio of displacement x to time interval t Subscript x indicates motion along x axis Dimensions: m/s (SI) x can be positive or negative
2.1 Average Velocity Average velocity can be interpreted geometrically A straight line can be drawn between any two points on curve Line forms the hypotenuse of right triangle of height x and base t Slope of hypotenuse is ratio x / t Average velocity during time interval t is slope of the line joining initial and final points on the position-time graph
2.1 Average Velocity The displacement of a particle during the time interval t i to t f is equal to the area under the curve between the initial and final points on a velocity-time curve
Example 2.1 Calculating the Average Velocity and Speed Find the displacement, average velocity, and average speed of the car between positions A and F. Find the displacement of the car: Find the car’s average velocity: Find the car’s average speed:
Example 2.2 Motion of a Jogger A jogger runs in a straight line, with an average velocity of magnitude 5.00 m/s for 4.00 min and then with an average velocity of magnitude 4.00 m/s for 3.00 min.
Example 2.2 Motion of a Jogger (A) What is the magnitude of the final displacement from her initial position? Find the displacement for each portion:
Example 2.2 Motion of a Jogger (B) What is the magnitude of her average velocity during this entire time interval of 7.00 min? Find the average velocity for the entire time interval:
2.2 Instantaneous Velocity Instantaneous velocity is 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
2.2 Instantaneous Velocity The instantaneous velocity is the slope of the line tangent to the x vs. t curve the green line in the figure The blue lines show that as t gets smaller, they approach the green line
2.2 Instantaneous Velocity

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