Unit #1: One Dimensional Kinematics Lesson 1: Describing motion with words Introduction to the Language of Kinematics Mechanics: the study of the motion of objects. Kinematics: is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. In this lesson, we will investigate the words used to describe the motion of objects. That is, we will focus on the language of kinematics. The hope is to gain a comfortable foundation with the language which is used throughout the study of mechanics. The words over the next few slides are used with regularity to describe the motion of objects. Your goal should be to become very familiar with their meaning.

Lesson 1: Describing motion with words Scalars and Vectors Words and phrases such as going fast, stopped, slowing down, speeding up, and turning provide a sufficient vocabulary for describing the motion of objects. In physics, we use these words and many more. We will be expanding upon this vocabulary list with words such as distance, displacement, speed, velocity, and acceleration. Scalars: quantities which are fully described by a magnitude or (numerical value) alone. Vectors: quantities which are fully described by both a magnitude and a direction. Check Your Understanding Categorize each quantity as being either a vector or a scalar. 5 m Scalar 30 m/sec, East Vector 5 mi., North Vector 20 degrees Celsius Scalar 256 bytes Scalar 4000 Calories Scalar

Lesson 1: Describing motion with words Distance and Displacement (HOW FAR) Distance and displacement are two quantities which may seem to mean the same thing yet have distinctly different definitions and meanings. Distance: a scalar quantity which refers to “how much ground an object has covered” during its motion. Displacement: a vector quantity which refers to “how far out of place an object is”; it is the object’s overall change in position. To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. What’s the teacher’s distance walked? 12m What’s the teacher’s displacement? 0m You can break down distance versus displacement here… if teacher just walks the 4 meters east, then distance IS displacement

Lesson 1: Describing motion with words Quick Quiz Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes. Distance: 420m Displacement: 140m rightward

Lesson 1: Describing motion with words Speed and Velocity (HOW FAST) Just as distance and displacement have distinctly different meanings (despite their similarities), so do speed and velocity. Speed a scalar quantity which refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. Velocity a vector quantity which refers to "the rate at which an object changes its position." If motion is in a straight line… then, speed=velocity Talk about + or – velocity (+ to right or up & - to left or down)

Lesson 1: Describing motion with words Calculating Average Speed and Average Velocity The average speed during the course of a motion is often computed using the following formula: Meanwhile, the average velocity is often computed using the equation Let's begin implementing our understanding of these formulas with the following problem: Q: While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? Why are they using “v” to represent speed here? Because they are assuming that the movement is in a straight line. Speed=velocity if movement is in a straight line

Lesson 1: Describing motion with words Quick Quiz Use the diagram to determine the average speed and the average velocity by the skier during these three minutes. Average Speed: (420 m) / (3 min) = 140 m/min Average Velocity: (140 m, right) / (3 min) = 46.7 m/min, right

Lesson 1: Describing motion with words Average Speed versus Instantaneous Speed Since a moving object often changes its speed during its motion, it is common to distinguish between the average speed and the instantaneous speed. The distinction is as follows. Instantaneous Speed the speed at any given instant in time. Average Speed the average of all instantaneous speeds; found simply by a distance/time ratio. Does a speedometer measure average speed or instantaneous speed? Instantaneous speed

Lesson 1: Describing motion with words Average Speed versus Instantaneous Speed The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure of the distance traveled in a given period of time. Suppose that during your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The average speed of your car could be determined as   On the average, your car was moving with a speed of 25 miles per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 miles per hour. Yet, on average, you were moving with a speed of 25 miles per hour.

Lesson 1: Describing motion with words Acceleration (HOW QUICKLY FAST CHANGES) The final mathematical quantity discussed in Lesson 1 is acceleration. An often confused quantity, acceleration has a meaning much different than the meaning associated with it by sports announcers and other individuals. Acceleration: A vector quantity which is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer. Both the green and blue cars show an acceleration.

Lesson 1: Describing motion with words The Meaning of Constant Acceleration Sometimes an accelerating object will change its velocity by the same amount each second. The data table to the right shows an object changing its velocity by 10 m/s in each consecutive second. A constant acceleration is when an object’s velocity changes by the same amount each second. Don’t confuse constant acceleration with constant velocity. Talk about difference between constant velocity and constant acceleration

Lesson 1: Describing motion with words Calculating Average Acceleration The average acceleration (a) of any object over a given interval of time (t) can be calculated using the equation This equation can be used to calculate the acceleration of the object whose motion is depicted by the velocity-time table. Typical acceleration units include the following: Units for speed is some unit of distance over some unit of time Units for acceleration is some unit of distance over some unit of time over some unit of time (rate at which velocity changes) m/s/s mi/hr/s km/hr/s m/s2

Lesson 1: Describing motion with words The Direction of the Acceleration Vector Since acceleration is a vector quantity, it has a direction associated with it. The direction of the acceleration vector depends on two things: 1. whether the object is speeding up or slowing down 2. whether the object is moving in the + or - direction The general RULE OF THUMB is: If an object is slowing down, then its acceleration is in the opposite direction of its motion. You can talk about the components of acceleration here (compare velocity and accel). When speeding up, velocity and accel in same direction. When slowing down, they are directed opposite one another. If slowing down, acceleration sign (+ or -) is directed opposite velocity sign. If speeding up, acceleration sign is same as velocity sign

Lesson 1: Describing motion with words The Direction of the Acceleration Vector Accelerations are positive when they act in the positive direction. (Be careful, positive accelerations do not always mean “speeding up”.) Accelerations are negative when they act in the negative direction. (Be careful, negative accelerations do not always mean “slowing down”.) Moving to right and speeding up… vel is + and accel is + Moving to right and slowing down… vel is + and accel is - Moving to left and speeding up… vel is – and accel is - Moving to left and slowing down… vel is – and accel is + ** Note: an accel vector representing object that is slowing down is always directed opposite of object motion

Lesson 1: Describing motion with words Check Your Understanding To test your understanding of the concept of acceleration, consider the following problems and the corresponding solutions. Use the equation for acceleration to determine the acceleration for the following two motions. Answer: a = 2 m/s/s Use a = (vf - vi) / t a = (8 m/s - 0 m/s) / (4 s) a = (8 m/s) / (4 s) a = 2 m/s/s Answer: a = -2 m/s/s Use a = (vf-vi) / t a = (0 m/s - 8 m/s) / (4 s) a = (-8 m/s) / (4 s) a = -2 m/s/s