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4.1 The Position, Velocity, and Acceleration Vectors The position of a particle by its position vector r, drawn from the origin of some coordinate system to the particle located in the xy plane Displacement vector:

4.1 The Position, Velocity, and Acceleration Vectors The average velocity: Note that the average velocity between points is independent of the path taken.

4.1 The Position, Velocity, and Acceleration Vectors The instantaneous velocity v: The magnitude of the instantaneous velocity vector is called the speed, which is a scalar quantity.

4.1 The Position, Velocity, and Acceleration Vectors The average acceleration: The instantaneous acceleration:

4.1 The Position, Velocity, and Acceleration Vectors

4.2 Two-Dimensional Motion with Constant Acceleration The position vector for a particle moving in the xy plane: The velocity of the particle

The equations of kinematics to the x and y components -Velocity vector as a function of time: Then:

The equations of kinematics to the x and y components Position vector as a function of time: Then:

The equations of kinematics to the x and y components These equations can be written in component form:

Example 4.1

4.4 Uniform Circular Motion Figure shows a car moving in a circular path with constant speed v. Such motion is called uniform circular motion. In circular motion, the velocity vector is changing in direction, so there an acceleration.

4.4 Uniform Circular Motion -An acceleration of circular motion is called a centripetal acceleration -The acceleration vector is perpendicular to the path, toward the center of the circle. - Centripetal Acceleration is not Constant

4.4 Uniform Circular Motion

Example 4.8

Question (1)

Question (2)

Question (18)

Question (21)

Question (22)

Problem (4.2)

Problem (5)

Problem (6)

Problem (27)