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Chapter 2

Chapter 2. Motion Along a Straight Line. Goals for Chapter 2. To describe straight-line motion in terms of velocity and acceleration To distinguish between average and instantaneous velocity and average and instantaneous acceleration

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Chapter 2

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  1. Chapter 2 Motion Along a Straight Line

  2. Goals for Chapter 2 • To describe straight-line motion in terms of velocity and acceleration • To distinguish between average and instantaneous velocity and average and instantaneous acceleration • To interpret graphs of position versus time, velocity versus time, and acceleration versus time for straight-line motion • To understand straight-line motion with constant acceleration • To examine freely falling bodies • To analyze straight-line motion when the acceleration is not constant

  3. Introduction • Kinematics is the study of motion. • Velocity and acceleration are important physical quantities. • A bungee jumper speeds up during the first part of his fall and then slows to a halt.

  4. Displacement, time, and average velocity—Figure 2.1 • A particle moving along the x-axis has a coordinate x. • The change in the particle’s coordinate is x = x2  x1. • The average x-velocity of the particle is vav-x = x/t. • Figure 2.1 illustrates how these quantities are related.

  5. Negative velocity • The average x-velocity is negative during a time interval if the particle moves in the negative x-direction for that time interval. Figure 2.2 illustrates this situation.

  6. A position-time graph—Figure 2.3 • A position-time graph (an x-t graph) shows the particle’s position x as a function of time t. • Figure 2.3 shows how the average x-velocity is related to the slope of an x-t graph.

  7. Instantaneous velocity—Figure 2.4 • The instantaneous velocity is the velocity at a specific instant of time or specific point along the path and is given by vx = dx/dt. • The average speed is not the magnitude of the average velocity!

  8. Average and instantaneous velocities • In Example 2.1, the cheetah’s instantaneous velocity increases with time. (Follow Example 2.1)

  9. Finding velocity on an x-t graph • At any point on an x-t graph, the instantaneous x-velocity is equal to the slope of the tangent to the curve at that point.

  10. Motion diagrams • A motion diagram shows the position of a particle at various instants, and arrows represent its velocity at each instant. • Figure 2.8 shows the x-t graph and the motion diagram for a moving particle.

  11. Average acceleration • Acceleration describes the rate of change of velocity with time. • The average x-acceleration is aav-x= vx/t. • Follow Example 2.2 for an astronaut.

  12. Instantaneous acceleration • The instantaneous accelerationis ax = dvx/dt. • Follow Example 2.3, which illustrates an accelerating racing car.

  13. Findingacceleration on a vx-t graph • As shown in Figure 2.12, the x-t graph may be used to find the instantaneous acceleration and the average acceleration.

  14. A vx-t graph and a motion diagram • Figure 2.13 shows the vx-t graph and the motion diagram for a particle.

  15. An x-t graph and a motion diagram • Figure 2.14 shows the x-t graph and the motion diagram for a particle.

  16. Motion with constant acceleration—Figures 2.15 and 2.17 • For a particle with constant acceleration, the velocity changes at the same rate throughout the motion.

  17. The equations of motion with constant acceleration • The four equations shown to the right apply to any straight-line motion with constant acceleration ax. • Follow the steps in Problem-Solving Strategy 2.1.

  18. A motorcycle with constant acceleration • Follow Example 2.4 for an accelerating motorcycle.

  19. Two bodies with different accelerations • Follow Example 2.5 in which the police officer and motorist have different accelerations.

  20. Freely falling bodies • Free fall is the motion of an object under the influence of only gravity. • In the figure, a strobe light flashes with equal time intervals between flashes. • The velocity change is the same in each time interval, so the acceleration is constant.

  21. A freely falling coin • Aristotle thought that heavy bodies fall faster than light ones, but Galileo showed that all bodies fall at the same rate. • If there is no air resistance, the downward acceleration of any freely falling object is g = 9.8 m/s2 = 32 ft/s2. • Follow Example 2.6 for a coin dropped from the Leaning Tower of Pisa.

  22. Up-and-down motion in free fall • An object is in free fall even when it is moving upward. • Follow Example 2.7 for up-and-down motion.

  23. Is the acceleration zero at the highest point?—Figure 2.25 • The vertical velocity, but not the acceleration, is zero at the highest point.

  24. Two solutions or one? • We return to the ball in the previous example. • How many solutions make physical sense? • Follow Example 2.8.

  25. Velocity and position by integration • The acceleration of a car is not always constant. • The motion may be integrated over many small time intervals to give

  26. Motion with changing acceleration • Follow Example 2.9. • Figure 2.29 illustrates the motion graphically.

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