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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 withConstant 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

Example 4.1

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

4.4 Uniform Circular Motion

Example 4.8

Question (1)

Question (2)

Question (18)

Question (21)

Question (22)

Problem (4.2)

Problem (4.2)

Problem (5)

Problem (6)

Problem (27)