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## Chapter 2

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**Chapter 2**Motion in One Dimension**2.1 Kinematics**• Describes motion while ignoring the agents that caused the motion • For now, will consider motion in one dimension • Along a straight line • Will use the particle model • A particle is a point-like object, has mass but infinitesimal size**Position 位置**• Defined in terms of a frame of reference • One dimensional, so generally the x- or y-axis • The object’s position is its location with respect to the frame of reference Fig 2.1(a)**Position-Time Graph**• The position-time graph shows the motion of the particle (car) • The smooth curve is a guess as to what happened between the data points Fig 2.1(b)**Displacement 位移**• Defined as the change in position during some time interval • Represented as x • SI units are meters (m) x can be positive or negative • Different than distance – the length of a path followed by a particle**Average Velocity 平均速度**• The average velocity is rate at which the displacement occurs • The dimensions are length / time [L/T] • The SI units are m/s • Is also the slope of the line in the position – time graph**Displacement from a Velocity - Time Graph**• The displacement of a particle during the time interval ti to tf is equal to the area under the curve between the initial and final points on a velocity-time curve Fig 2.1(c)**Active Figure**2.1 • If you can't see the image above, please install Shockwave Flash Player. • If this active figure can’t auto-play, please click right button, then click play. NEXT**瞬時速度2.2 Instantaneous 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**Instantaneous Velocity, graph**• The instantaneous velocity is the slope of the line tangent to the x vs. t curve • This would be the green line • The blue lines show that as t gets smaller, they approach the green line Fig 2.2(b)**Active Figure**2.2 • If you can't see the image above, please install Shockwave Flash Player. • If this active figure can’t auto-play, please click right button, then click play. NEXT**Instantaneous Velocity, equations**• The general equation for instantaneous velocity is**Instantaneous Velocity, Signs**• At point A, vx is positive • The slope is positive • At point B, vx is zero • The slope is zero • At point C, vx is negative • The slope is negative Fig 2.3**Instantaneous Speed**• The instantaneous speed is the magnitude of the instantaneous velocity vector • Speed can never be negative • Thinking Physics 2.1(P.43)**2.3 Constant Velocity**• If the velocity of a particle is constant • Its instantaneous velocity at any instant is the same as the average velocity over a given time period • vx = vx,avg = Dx / Dt • Also, xf = xi + vxt • These equations can be applied to particles or objects that can be modeled as a particle moving under constant velocity**2.4 Average Acceleration**• Acceleration is the rate of change of the velocity • It is a measure of how rapidly the velocity is changing • Dimensions are L/T2 • SI units are m/s2**Instantaneous Acceleration**• The instantaneous acceleration is the limit of the average acceleration as t approaches 0**Instantaneous Acceleration – Graph**• The slope of the velocity vs. time graph is the acceleration • Positive values correspond to where velocity in the positive x direction is increasing • The acceleration is negative when the velocity is in the positive x direction and is decreasing Fig 2.7**QUICK QUIZ 2.3**Match each of the velocity-time graphs on the top with the acceleration-time graphs on the bottom. Fig 2.8**Active Figure**2.8 • If you can't see the image above, please install Shockwave Flash Player. • If this active figure can’t auto-play, please click right button, then click play. NEXT**Fig 2.9**The velocity of the car decrease from 30 m/s to 15 m/s in a time interval of 2.0 s a =?**2.5 Negative Acceleration**• Negative acceleration does not necessarily mean that an object is slowing down • If the velocity is negative and the acceleration is negative, the object is speeding up • Deceleration is commonly used to indicate an object is slowing down, but will not be used in this text**Acceleration and Velocity, 1**• When an object’s velocity and acceleration are in the same direction, the object is speeding up in that direction • When an object’s velocity and acceleration are in the opposite direction, the object is slowing down**2.6 Kinematic Equations**Fig 2.12**Active Figure**2.11 • If you can't see the image above, please install Shockwave Flash Player. • If this active figure can’t auto-play, please click right button, then click play. NEXT**Kinematic Equations**• The kinematic equations may be used to solve any problem involving one-dimensional motion with a constant acceleration • You may need to use two of the equations to solve one problem • The equations are useful when you can model a situation as a particle under constant acceleration