Chapter 2: Kinematics - Description of Motion

1. Chapter 2 Kinematics: Description of Motion August 23 Scalars and vectors 2.1 Distance and Speed: Scalar Quantities Distance is the path length traveled from one location to another. It varies depending on the actual path. Distance is a scalar quantity. A scalar quantity has only magnitude. This magnitude may be positive or negative. Examples: distance, time, mass, temperature, energy, electric current. Average speed is the distance traveled divided by the elapsed time: In physics, D stands for the change in a quantity (new value subtracts the old one). Speed is a scalar. Example: Driving from Macomb to Chicago, 246 miles in 4 hours.

2. Instantaneous speed is the speed measured over a very short time interval. It measures how fast an object is moving at a particular instant of time. This is what a speedometer reads. This is also what the speed limit on a high way means. • 2.2 One-Dimensional Displacement and Velocity: Vector Quantities • A vector has both magnitude and direction. Manipulating vectors requires a coordinate system, as shown in the diagram. • Examples: velocity, acceleration, momentum. • In printing, bold letters (like v) are used for vectors. In handwriting, it is This convention must be followed. • Vectors may have different components if we use a different coordinate system, but the vector itself (magnitude and direction) does not change. • Vectors are better understood when they are two- or three-dimensional, which is left to future chapters. • When you are introduced a physical quantity, remember its physical meaning, algebraic definition, unit, and whether it’s a scalar or vector (sometimes tensor).

3. B Displacement is a vector that points from the initial position to the final position of an object, regardless of the actual path the object moves. Velocity is a vector that describes how fast an object is moving and in which direction it is moving. Average velocity is the displacement divided by the total travel time. In one dimension it is A Example 2.2: There and Back: Average Velocities Instantaneous velocity is the average velocity in a very short time interval: Graphical analysis: In a position-versus-time graph, the slope of the curve indicates the velocity of the object. The two graphs here show a uniform motion and a non-uniform motion.

4. Read: Ch2: 1-2 Homework: Ch2: E2,9,14 Due: August 30

5. August 26 Acceleration 2.3 Acceleration Acceleration is the rate at which velocity changes. It measures how faster and faster an object moves. Average acceleration is the change in velocity divided by the elapsed time: The SI unit of acceleration is m/s2 (meter per second-squared). Instantaneous acceleration is then Acceleration is a vector, its direction is parallel to , the change of the velocity.

6. Acceleration means that the speed of an object is changing, or its direction is, or both (Figure 2.9). Acceleration may result in an object either speeding up or slowing down, or simply changing its direction. Example: elevator, circular motion, orbital motion.

7. In constant acceleration, a does not change with time, from the definition of acceleration, the velocity of the object is then given by The average velocity is In a velocity-versus-time graph, the slope of the curve indicates the acceleration of the object (Fig. 2.10). Example 2.5: On the Water: Using Multiple Equations

8. 2.4 Kinematic Equations (Constant Acceleration) At constant acceleration, from previous equations, we have The correct equation for solving a problem should be selected considering the information given and the desired result. In many cases one equation can be much easier than other equations.

9. Example 2.7: Moving Apart: Where Are They Now? Example2.8: Putting On the Brakes: Vehicle Stopping Distance. Please note this example asks for an expression rather than a numerical solution. We will have more such practices in class.

10. Read: Ch2: 3-4 Homework: Ch2: E33,40,44 Due: September 6

11. August 27 Free Fall 2.4 Free Fall • Objects in motion solely under the influence of gravity are said to be in free fall.An object in free fall has a constant acceleration (in the absence of air resistance) due to the Earth’s gravity. This acceleration is directed downwardwith an magnitude of • , which is called the acceleration due to gravity. • The value of g varies slightly at different locations on the earth, depending on the altitude and elevation of the location. It also depends on whether you are on the earth. • The set of equations for motion with constant acceleration that we have learned can be directly used to solve free fall problems: Taking y as the motion direction and taking upward as positive. a= −g = −9.8m/s2. Note different conventions exist.

12. The constancy of the acceleration due to gravity regardless of the weights of the objects were first recognized by Galileo Galilei. Demo: Accelerations in free fall (heavy ball and light ball, ball and paper, water cup). Galileo Galilei (1564-1642)

13. Example 2.9: A Stone Thrown Downward :The Kinematic Equations Revisited Example 2.10: Measuring Reaction Time: Free Fall Example2.11: Free Fall Up and Down: Using Implicit Data

14. Read: Ch2: 5 Homework: Ch2: E59,63,68 Due: September 6

15. Tout le malheur des hommes vient d’une seule chose, qui est de ne savoir pas demeurer en repos dans une chambre. All men's miseries derive from not being able to sit in a quiet room alone. Blaise Pascal