Chapter 2 Kinematics: Description of Motion

Units of Chapter 2 Distance and Speed: Scalar Quantities One-Dimensional Displacement and Velocity: Vector Quantities Acceleration Kinematic Equations (Constant Acceleration) Free Fall

2.1 Distance and Speed: Scalar Quantities Distance is the path length traveled from one location to another. It will vary depending on the path. Distance is a scalar quantity—it is described only by a magnitude.

2.1 Distance and Speed: Scalar Quantities Average speed is the distance traveled divided by the elapsed time:

2.1 Distance and Speed: Scalar Quantities Since distance is a scalar, speed is also a scalar (as is time). Instantaneous speed is the speed measured over a very short time span. This is what a speedometer reads.

2.2 One-Dimensional Displacement and Velocity: Vector Quantities A vector has both magnitude and direction. Manipulating vectors means defining a coordinate system, as shown in the diagrams to the left.

2.2 One-Dimensional Displacement and Velocity: Vector Quantities Displacement is a vector that points from the initial position to the final position of an object.

2.2 One-Dimensional Displacement and Velocity: Vector Quantities Note that an object’s position coordinate may be negative, while its velocity may be positive; the two are independent.

2.2 One-Dimensional Displacement and Velocity: Vector Quantities For motion in a straight line with no reversals, the average speed and the average velocity are the same. Otherwise, they are not; indeed, the average velocity of a round trip is zero, as the total displacement is zero!

2.2 One-Dimensional Displacement and Velocity: Vector Quantities Different ways of visualizing uniform velocity:

2.2 One-Dimensional Displacement and Velocity: Vector Quantities This object’s velocity is not uniform. Does it ever change direction, or is it just slowing down and speeding up?

2.3 Acceleration Acceleration is the rate at which velocity changes.

2.3 Acceleration Acceleration means that the speed of an object is changing, or its direction is, or both.

2.3 Acceleration Acceleration may result in an object either speeding up or slowing down (or simply changing its direction).

2.3 Acceleration If the acceleration is constant, we can find the velocity as a function of time:

2.4 Kinematic Equations (Constant Acceleration) From previous sections:

2.4 Kinematic Equations (Constant Acceleration) Substitution gives: and:

2.4 Kinematic Equations (Constant Acceleration) These are all the equations we have derived for constant acceleration. The correct equation for a problem should be selected considering the information given and the desired result.

2.5 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 downward.

2.5 Free Fall The effects of air resistance are particularly obvious when dropping a small, heavy object such as a rock, as well as a larger light one such as a feather or a piece of paper. However, if the same objects are dropped in a vacuum, they fall with the same acceleration.

2.5 Free Fall Here are the constant-acceleration equations for free fall: The positive y-direction has been chosen to be upwards. If it is chosen to be downwards, the sign of g would need to be changed.

Summary of Chapter 2 Motion involves a change in position; it may be expressed as the distance (scalar) or displacement (vector). A scalar has magnitude only; a vector has magnitude and direction. Average speed (scalar) is distance traveled divided by elapsed time. Average velocity (vector) is displacement divided by total time.

Summary of Chapter 2 Instantaneous velocity is evaluated at a particular instant. Acceleration (vector) is the time rate of change of velocity. Kinematic equations for constant acceleration:

Summary of Chapter 2 An object in free fall has a = –g. Kinematic equations for an object in free fall: