Slide 1 / 113 Slide 2 / 113 Kinematics in 1-Dimension www.njctl.org Slide 3 / 113 Slide 4 / 113 How to Use this File Table of Contents Click on the topic to go to that section Each topic is composed of brief direct instruction · There are formative assessment questions after every topic · What is Kinematics? · denoted by black text and a number in the upper left. Displacement and Distance · > Students work in groups to solve these problems but use Velocity and Speed student responders to enter their own answers. · Acceleration · > Designed for SMART Response PE student response systems. Free Fall · Kinematics Equations · > Use only as many questions as necessary for a sufficient number of students to learn a topic. Velocity and Position by Integration · Position-Time Graph Interpretation · Full information on how to teach with NJCTL courses can be · found at njctl.org/courses/teaching methods Slide 5 / 113 Slide 6 / 113 Terms Kinematics is the study of the motion of objects. It doesn't care What is Kinematics? what is making the objects move - that's the topic of the next chapter - Dynamics. Before we can launch into the study of Kinematics, we need to define position, and the mathematical terms scalar and vector. Return to Table of Contents
Slide 7 / 113 Slide 8 / 113 Position Position - Time graph and chart This chapter will focus on 1- To know how an object moves, you need to know its position at all Dimensional motion, so an times. appropriate reference frame will be the x axis (or y axis if You measure position by choosing a reference frame and noting the object is moving up and how far and in what direction the object is from a specific point on down). the reference frame - typically the origin. Since we need to know its Most of the time a Cartesian coordinate system works (x, y, z), but position at all times, we can you can also use a polar coordinate system (r, θ). either use a table, listing its position, or a graph. It is easier to visualize the actual motion using a graph - a Position - Time graph. Slide 9 / 113 Slide 10 / 113 1 At what time is the object's position equal to 6.0 m? Scalar and Vector A 2.0 s One more formalism before we get into describing motion. There are two terms that are used to describe where an object B 2.5 s is located and how it moves. C 3.0 s Scalar - this gives the magnitude of the motion - it has no · D 3.5 s direction. Scalar variables include time and energy - quantities that have no direction. Note - scalar values may be positive or negative, but they don't indicate direction. Vector - this is a combination of the magnitude and the · direction in which the motion changes. Most physics problems will involve the use of vectors. Slide 10 (Answer) / 113 Slide 11 / 113 1 At what time is the object's position equal to 6.0 m? 2 What is the object's position at t = 3.4 s? A 2.0 s A 8.0 m B 2.5 s B 10 m C 3.0 s C 12 m Answer B D 3.5 s D 14 m [This object is a pull tab]
Slide 11 (Answer) / 113 Slide 12 / 113 2 What is the object's position at t = 3.4 s? 3 Compare and contrast the properties of scalar and vector quantities. Students type their answers here A 8.0 m B 10 Answer m C C 12 m D 14 m [This object is a pull tab] Slide 12 (Answer) / 113 Slide 13 / 113 3 Compare and contrast the properties of scalar and vector quantities. Students type their answers here Displacement and Distance Both quantities have a magnitude (size), but a vector has a direction, Answer and a scalar does not have a direction. A scalar may be positive or negative, and they add algebraically, but there is no direction implied. [This object is a pull tab] Return to Table of Contents Slide 14 / 113 Slide 15 / 113 Displacement and Distance Displacement and Distance To show the difference between distance and displacement, Distance is a measure of how far an object travels without regard to consider the below sketch. It shows the motion of an object its initial or final position. It is a scalar quantity, and is frequently from to . labeled "d". (Displacement) Displacement is quite different. It measures the difference between an object's final and initial positions. It is a vector and has direction and magnitude and is labeled . Different variables are used in 2 and 3 dimensional problems. Motion is in this direction Both quantities are measured in meters (m). The displacement is in the positive direction (or the east or to the right or any relevant direction description). Displacement ≡ In this case, the magnitude of the displacement is equal to the distance traveled by the object. The distance is just a number with appropriate units (m, in this case) - it has no direction.
Slide 16 / 113 Slide 17 / 113 Displacement and Distance Displacement and Distance Consider the following case where the magnitude of the = (-4 - 0) m = -4 m, or 4 m in the negative direction displacement will NOT equal the distance traveled. An object or 4 m to the left or 4 m West - depending on how the problem starts at zero, moves 9 units to the right (red), then 13 units to is asked - please check with your instructor for his/her the left (green). What is its displacement, ? What is the preference (represented by the blue line). distance, d, traveled? d = (9 + 13) m = 22 m (represented by the sum of the red and green lines, without regard to sign, and with no direction - the total distance traveled). -5 0 5 10 -5 10 0 5 Distance does not have to equal the magnitude of the displacement! Slide 18 / 113 Slide 18 (Answer) / 113 4 How far your final position is from your initial position is 4 How far your final position is from your initial position is known as: known as: A distance A distance B displacement B displacement Answer B C scalar C scalar D vector D vector [This object is a pull tab] Slide 19 / 113 Slide 19 (Answer) / 113 5 How far you physically travel is called: 5 How far you physically travel is called: A distance A distance B displacement B displacement Answer A C scalar C scalar D vector D vector [This object is a pull tab]
Slide 20 / 113 Slide 20 (Answer) / 113 6 A car travels 5500 m to the north, and then 3200 m to the 6 A car travels 5500 m to the north, and then 3200 m to the south. What distance was traveled by the car? south. What distance was traveled by the car? Answer 8700 m [This object is a pull tab] Slide 21 / 113 Slide 21 (Answer) / 113 7 A car travels 5500 m to the north, and then 3200 m to the 7 A car travels 5500 m to the north, and then 3200 m to the south. What was the displacement of the car? south. What was the displacement of the car? Answer 2300 m to the north [This object is a pull tab] Slide 22 / 113 Slide 22 (Answer) / 113 8 You run around a 400 m track. At the end of the race, 8 You run around a 400 m track. At the end of the race, what is the distance that you traveled? what is the distance that you traveled? Answer 400 m [This object is a pull tab]
Slide 23 / 113 Slide 23 (Answer) / 113 9 You run around a 400 m track. At the end of the race, 9 You run around a 400 m track. At the end of the race, what is your displacement? what is your displacement? Answer 0 m [This object is a pull tab] Slide 24 / 113 Slide 25 / 113 Average Velocity and Speed The next quantities to be defined are average velocity and Velocity and Speed average speed, and they represent, respectively, the change in displacement and the change in distance over time. Average velocity (x direction): Average speed: Time is a scalar. So what does that tell you about average velocity and average speed? Velocity and speed are used in everyday language, but they Return to Table have distinct definitions in physics. of Contents Slide 26 / 113 Slide 27 / 113 10 One object has a velocity of 5.0 m/s. Another object has Average Velocity and Speed a velocity of -5.0 m/s. Do they have the same speed? Since displacement is a vector, when you divide it by a scalar, the Yes result is a vector; average velocity is a vector. No Since distance is a scalar, when you divide it by a scalar, the result is a scalar; average speed is a scalar. Speed can, but does not have to, equal the magnitude of velocity. Velocity is more useful in Physics.
Slide 27 (Answer) / 113 Slide 28 / 113 10 One object has a velocity of 5.0 m/s. Another object has 11 A particle is at position, x 0 = 19 m at t 0 = 1.0 s, and is at a velocity of -5.0 m/s. Do they have the same speed? position, x f = 277 m at t = 4.0 s. Find the average velocity and the average speed. Yes No Answer Yes [This object is a pull tab] Slide 28 (Answer) / 113 Slide 29 / 113 11 A particle is at position, x 0 = 19 m at t 0 = 1.0 s, and is at 12 A particle is at position, x 0 = 19 m at t 0 = 1.0 s, and is at position, x f = 277 m at t = 4.0 s. Find the average position, x f = -277 m at t = 4.0 s. Find the average velocity and the average speed. velocity and the average speed. in the positive x direction Answer In this case, the speed is equal to the magnitude of the velocity. [This object is a pull tab] Slide 29 (Answer) / 113 Slide 30 / 113 13 A particle is at position, x 0 = 0 m at t 0 = 1.0 s, and is at position, x f = -277 m at t = 4.0 s. Find the average velocity and the average speed.
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