ppt_chapter03.ppt - Raymond A Serway John W Jewett Chapter 3 Motion in Two Dimensions 3.1 The Position Velocity and Acceleration Vectors • • The

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Raymond A. Serway John W. Jewett Chapter 3 Motion in Two Dimensions
3.1 The Position, Velocity, and Acceleration Vectors The position of an object is described by its position vector The displacement of the object is the difference between its final and initial positions:
3.1 The Position, Velocity, and Acceleration Vectors The average velocity is the ratio of the displacement to the time interval for the displacement: The direction of the average velocity is the direction of the displacement vector
3.1 The Position, Velocity, and Acceleration Vectors The average velocity between points is independent of the path taken This is because it is dependent on the displacement, which is also independent of the path If a particle starts its motion at some point and returns to this point via any path, its average velocity is zero for this trip since its displacement is zero
3.1 The Position, Velocity, and Acceleration Vectors The instantaneous velocity is the limit of the average velocity as ∆ t approaches zero: The direction of the instantaneous velocity vector at any point in a particle’s path is along a line tangent to the path at that point and in the direction of motion The magnitude of the instantaneous velocity vector is the speed
3.1 The Position, Velocity, and Acceleration Vectors The average acceleration of a particle is the ratio of the change in the instantaneous velocity to the time interval:
3.1 The Position, Velocity, and Acceleration Vectors As a particle moves, v can be found in different ways, according to the rules of vector addition The average acceleration is a vector quantity directed along v
3.1 The Position, Velocity, and Acceleration Vectors The instantaneous acceleration is the limit of the average acceleration as v / t approaches zero:
3.1 The Position, Velocity, and Acceleration Vectors Various changes in a particle’s motion may produce an acceleration The magnitude of the velocity vector may change The direction of the velocity vector may change Even if the magnitude remains constant Both may change simultaneously
3.2 Two-Dimensional Motion with Constant Acceleration When the two-dimensional motion has a constant acceleration, a series of equations can be developed that describe the motion These equations will be similar to those of one- dimensional kinematics Motion in two dimensions can be modeled as two independent motions in the x and y directions Any influence in the y direction does not affect the motion in the x direction, and vise versa
3.2 Two-Dimensional Motion with Constant Acceleration Position vector: Velocity: Since acceleration is constant, we can also find an expression for the velocity as a function of time: The position vector as a function of time can be written as
3.2 Two-Dimensional Motion with Constant Acceleration The velocity and position vectors can be represented by components:
Example 3.1 Motion in a Plane

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