Physics
Time Speed and Distance
Time, speed, and distance are interrelated concepts in physics. Time is the duration of an event, speed is the rate at which an object moves, and distance is the amount of space between two points. These concepts are used to calculate the motion of objects and the time it takes for them to travel a certain distance at a certain speed.
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9 Key excerpts on "Time Speed and Distance"
eBook - PDFEngineering Science N2 Student's Book
TVET FIRST
- MJJ van Rensburg(Author)
- 2016(Publication Date)
- Troupant(Publisher)
1 M O D U L E Dynamics 1 Unit 1.1: Distance, displacement, speed, velocity, acceleration and time Setting the scene Figure 1.1: A car’s odometer measures the distance covered while the speedometer measures the instantaneous speed 1. You travel 567 km on the N3 from Johannesburg to Durban. Is this a measure of the distance or displacement between the two cities? 2. You use a GPS to calculate the shortest route between two towns. Is this a measure of the distance or displacement between the two towns? 3. What is the difference between instantaneous speed and average speed? Objectives and overview When you have completed Unit 1.1, you should be able to: • Distinguish between distance and displacement, and between speed and velocity, and briefly describe each of these concepts. • Indicate the relationship between distance, speed and time by means of a simple formula, and manipulate and apply this formula ( speed = distance time ) . • Indicate the relationship between displacement, velocity and time by means of a simple formula, and manipulate and apply this formula ( velocity = displacement time ) . • Define acceleration, and write it in the form of a simple formula ( a = Δ v Δ t ) , which must be manipulated and applied. • Classify the quantities: distance, speed, displacement, velocity, acceleration and time, as scalars or vectors, according to their properties. 2 Basic concepts Dynamics is the branch of science that is concerned with the study of forces and their effect on motion. To understand the science of dynamics, you must not only know the basic concepts but also be able to distinguish between them. In this unit, we will distinguish between concepts such as distance and displacement, speed and velocity, scalars and vectors. We will also look at other concepts relevant to the field of dynamics. Note In this book, the unit symbols are often used interchangeably.
eBook - PDFTime and Human Cognition
A Life-Span Perspective
- I. Levin, D. Zakay(Authors)
- 1989(Publication Date)
- North Holland(Publisher)
WHAT UNDERSTANDING ENTAILS Time, speed and distance form a closed system in our universe. If one dimension is held constant, then a qualitative change in one of the remain- ing two dimensions necessitates a qualitative change in the other. Both speed and time bear direct (i.e., positive) relations to distance: if the dura- tion of travel is held constant, greater speeds yield farther distances, while 222 CHAPTER 6. TIME-SPEEDDISTANCE INTERRELATIONS if speed is constant, greater durations of travel yield farther distances. But time bears an inverse (i.e., negative) relation to speed if distance is held constant, greater durations require slower speeds. As a matter of conveni- ence, we may use the term bivariate to refer to the necessary qualitative relations between pairs of dimensions when the third variable is held con- stant. What happens when all three dimensions are allowed to vary? Trav- eling a farther distance at a slower speed invariably leads to a longer dura- tion but traveling a farther distance at a faster speed may lead to a longer, shorter or the same duration. In this latter case, there is no one necessary solution. Again, as a matter of convenience, we may use the term trivariate to refer to the necessary qualitative relations among dimensions when all three are allowed to vary. A complete understanding of the necessary in- terrelations between time, speed and distance implies mastery of both the bivariate and the trivariate relations. It is possible, though not certain, that children may grasp the bivariate relations before the trivariate relations, rather than contemporaneously. That is, they may develop an understanding that greater distances always yield longer durations whenever speeds are held constant, and greater speeds always yield shorter durations whenever distances are held con- stant, but admit to uncertainty when all three variables are allowed to vary.
eBook - PDFA Basic Theory of Everything
A Fundamental Theoretical Framework for Science and Philosophy
- Atle Ottesen Søvik(Author)
- 2022(Publication Date)
- De Gruyter(Publisher)
With a common currency of, for example, feet or meters, together with numbers, all objects can be compared in size, and a unit of measuring size or space is born. The size of any object or the distance between any objects can now be described as a number expressed in meters. Objects are experienced to move relative to each other. Some motions are constant compared to each other, and some things move faster than others. The earth orbiting the sun moves as fast as the earth takes to spin around itself 365 times, and some can run in one day a distance that others need two days to run. Using many different constant motions that have a constant relation to each other, we can define one constant motion to be used as a measure of all other motions. The thing in motion must cover a distance, which can then be divided into units of time. For example, the earth covering the distance of spinning around its own axis once can be divided into 24 parts called hours, which can be divided into 60 parts called minutes, which can be divided into 60 parts called seconds. With this constant motion giving us units of seconds, minutes, hours, etc., we can now compare all other motions with this motion to describe their speed. The speed will then be a measure of distance divided by time, for example kilometers per hour or meters per second.²⁴⁰ Any speed can be described with a number (in physics called a “scalar”) and meters per second, or m/s.²⁴¹ I am simplifying matters here for pedagogical reasons, since I want the reader to see the development starting with meter and second and then moving to the other concepts. That is why I use the units meter and second for speed and acceleration instead of saying distance div- ided by time. I am also for simplicity just talking about speed here instead of distinguishing be- tween speed and velocity, where velocity is an amount of speed in a direction, while speed only is the numerical value of the velocity.
eBook - PDF- Vern Ostdiek, Donald Bord(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
Velocity is an example of a physical quantity called a vector. Vectors have both a numerical size (magnitude) and a direction associated with them. Quantities that do not have a direction are called scalars. Speed by itself is a scalar. Only when the direction of motion is included do we have the vector velocity. Similarly, we can define the vector displacement as Table 1.2 Some Speeds of Interest Description Metric English Speed of light, c (in vacuum) c c 3 3 10 8 m/s 186,000 miles/second Speed of sound (in air, room temperature) 344 m/s 771 mph Highest instantaneous speeds: Running (cheetah) 28 m/s 75 mph Swimming (sailfish) 30.6 m/s 68 mph Flying—level (merganser) 36 m/s 80 mph Flying—dive (peregrine falcon) 108 m/s 242 mph Humans (approximate): Swimming 2.5 m/s 5.6 mph Running 12 m/s 27 mph Ice skating 14 m/s 31 mph Figure 1.9 Hand-held GPS receiver capable of measuring speed and direction of motion, that is, velocity. Ovu0ng/Shutterstock.com Velocity Speed in a particular direction (same units as speed). Directed motion. DEFINITION Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 22 Chapter 1 The Study of Motion distance in a specific direction. For the airplane referred to earlier, the distance it travels in 2 hours is 200 miles. Its ac e e - tual location can be determined only from its displacement— t t 200 miles due north, for example. The basic equation for speed, v 5 Dd/ Dt, is also the equation for velocity (that’s why v is used) v v with d representing a vector displacement. We can classify most physical quantities as scalars or vectors. Time, mass, and volume are all scalars because there is no direc- tion associated with them. Vectors are represented by arrows in drawings, the length of the arrow being proportional to the size or magnitude of the vector (Figure 1.10).
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
2.3 | Define one-dimensional acceleration. 2.4 | Use one-dimensional kinematic equations to predict future or past values of variables. 2.5 | Solve one-dimensional kinematic problems. 2.6 | Solve one-dimensional free-fall problems. 2.7 | Predict kinematic quantities using graphical analysis. 23 24 Chapter 2 | Kinematics in One Dimension direction is assigned a negative value. For instance, assume that a car is moving along an east/west direction and that a positive (1) sign is used to denote a direction due east. Then, D x B 5 1500 m represents a displacement that points to the east and has a magnitude of 500 meters. Conversely, D x B 5 2500 m is a displacement that has the same magnitude but points in the opposite direction, due west. The magnitude of the displacement vector is the shortest distance between the ini- tial and final positions of the object. However, this does not mean that displacement and distance are the same physical quantities. In Figure 2.1, for example, the car could reach its final position after going forward and backing up several times. In that case, the total distance traveled by the car would be greater than the magnitude of the displacement vector. Check Your Understanding (The answer is given at the end of the book.) 1. A honeybee leaves the hive and travels a total distance of 2 km before returning to the hive. What is the magnitude of the displacement vector of the bee? 2.2 | Speed and Velocity Average Speed One of the most obvious features of an object in motion is how fast it is moving. If a car travels 200 meters in 10 seconds, we say its average speed is 20 meters per second, the av- erage speed being the distance traveled divided by the time required to cover the distance: Average speed 5 Distance Elapsed time (2.1) Equation 2.1 indicates that the unit for average speed is the unit for distance divided by the unit for time, or meters per second (m/s) in SI units. Example 1 illustrates how the idea of average speed is used.
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
If the elapsed time is known, then two additional quantities can be calculated—that is, average speed and average velocity, which are related to the rate at which distance is covered and the rate at which position changes, respectively. I N T E R A C T I V E F E A T U R E I N T E R A C T I V E F E A T U R E Average Speed and Velocity | 47 Average Speed Consider again the runner on the sidewalk. Suppose that he is jogging slowly in the positive x direction (Figure 2.2.1). He wants to determine how fast he can run, so he sprints from the stop sign to the yield sign. The distance he travels is simply the straight-line distance between the signs. 53.0 m +x Figure 2.2.1 Average speed equals the length of travel (distance) divided by the time interval over which that distance was covered. The runner’s average speed is equal to the distance traveled divided by the time interval over which that distance was covered: average speed distance elapsed time = (2.2.1) The SI units of average speed are meters per second, m/s. In Figure 2.2.1, the distance between the signs is 53.0 m and the runner covers that distance in 8.50 s, so his average speed is ( ) ( ) 53.0 m 8.50 s 6.24 m s / / = . Example 2.2.1 shows how to use Equation 2.2.1 to calculate distances. Example 2.2.1 Calculating Distance from Speed While you are driving on the highway, the speed limit changes from 95 km/h to 75 km/h. If you maintain the speed limit for 13 min at each speed, what is the total distance traveled? Identify The total distance can be given in units of km or m. The same amount of time is spent at each speed, so the majority of the distance is covered while traveling at the higher speed. Plan The total distance is equal to the sum of the distances traveled at each speed.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
However, all of the questions are available for assignment via WileyPLUS. Section 2.1 Displacement 1. What is the difference between distance and displacement? (a) Distance is a vector, while displacement is not a vector. (b) Displacement is a vector, while distance is not a vector. (c) There is no difference between the two concepts; they may be used interchangeably. Section 2.2 Speed and Velocity 3. A jogger runs along a straight and level road for a distance of 8.0 km and then runs back to her starting point. The time for this round-trip is 2.0 h. Which one of the following statements is true? (a) Her average speed is 8.0 km/h, but there is not enough information to determine her average velocity. (b) Her average speed is 8.0 km/h, and her average velocity is 8.0 km/h. (c) Her average speed is 8.0 km/h, and her average velocity is 0 km/h. Section 2.3 Acceleration 6. The velocity of a train is 80.0 km/h, due west. One and a half hours later its velocity is 65.0 km/h, due west. What is the train’s average acceleration? (a) 10.0 km/h 2 , due west (b) 43.3 km/h 2 , due west (c) 10.0 km/h 2 , due east (d) 43.3 km/h 2 , due east (e) 53.3 km/h 2 , due east. Section 2.4 Equations of Kinematics for Constant Acceleration 10. In which one of the following situations can the equations of kinematics not be used? (a) When the velocity changes from moment to moment, (b) when the velocity remains constant, (c) when the acceleration changes from moment to moment, (d) when the acceleration remains constant. 13. In a race two horses, Silver Bullet and Shotgun, start from rest and each maintains a constant acceleration. In the same elapsed time Silver Bullet runs 1.20 times farther than Shotgun.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
CHAPTER 2 Kinematics in one dimension LEARNING OBJECTIVES After reading this module, you should be able to: 2.1 define one‐dimensional displacement 2.2 discriminate between speed and velocity 2.3 define one‐dimensional acceleration 2.4 use one‐dimensional kinematic equations to predict future or past values of variables 2.5 solve one‐dimensional kinematic problems 2.6 solve one‐dimensional free‐fall problems 2.7 predict kinematic quantities using graphical analysis. INTRODUCTION Australia holds the world record for the longest section of straight railway track: 478 kilometres of the Trans- Australian Railway that traverses the Nullarbor Plain between Sydney and Perth without a single curve. Drivers must stay vigilant for wandering kangaroos and camels as they speed across the endless kilometres of dead straight track, pressing a red ‘dead man’ switch every minute or so for safety. In this chapter we take a look at the properties of straight-line motion, such as displacement, velocity and acceleration. 1 2.1 Displacement LEARNING OBJECTIVE 2.1 Define one-dimensional displacement. There are two aspects to any motion. In a purely descriptive sense, there is the movement itself. Is it rapid or slow, for instance? Then, there is the issue of what causes the motion or what changes it, which requires that forces be considered. Kinematics deals with the concepts that are needed to describe motion, without any reference to forces. The present chapter discusses these concepts as they apply to motion in one dimension, and the next chapter treats two‐dimensional motion. Dynamics deals with the effect that forces have on motion, a topic that is considered in chapter 4. Together, kinematics and dynamics form the branch of physics known as mechanics. We turn now to the first of the kinematics concepts to be discussed, which is displacement. FIGURE 2.1 The displacement Δ x is a vector that points from the initial position x 0 to the final position x.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Example 1 illustrates how the idea of average speed is used. EXAMPLE 1 | Distance Run by a Jogger How far does a jogger run in 1.5 hours (5400 s) if his average speed is 2.22 m/s? Reasoning The average speed of the jogger is the average distance per second that he travels. Thus, the distance covered by the jogger is equal to the average distance per second (his average speed) multiplied by the number of seconds (the elapsed time) that he runs. Solution To find the distance run, we rewrite Equation 2.1 as Distance 5 (Average speed)(Elapsed time) 5 (2.22 m/s)(5400 s) 5 12 000 m Speed is a useful idea, because it indicates how fast an object is moving. However, speed does not reveal anything about the direction of the motion. To describe both how fast an object moves and the direction of its motion, we need the vector concept of velocity. Average Velocity To define the velocity of an object, we will use two concepts that we have already encoun- tered, displacement and time. The building of new concepts from more basic ones is a common theme in physics. In fact the great strength of physics as a science is that it builds a coherent understanding of nature through the development of interrelated concepts. Suppose that the initial position of the car in Figure 2.1 is x B 0 when the time is t 0 . A little later that car arrives at the final position x B at the time t. The difference between these times is the time required for the car to travel between the two positions. We denote this 28 Chapter 2 | Kinematics in One Dimension difference by the shorthand notation Dt (read as “delta t”), where Dt represents the final time t minus the initial time t 0 : D t 5 t 2 t 0 Elapsed time Note that Dt is defined in a manner analogous to D x B , which is the final position minus the initial position (D x B 5 x B 2 x B 0 ). Dividing the displacement D x B of the car by the elapsed time Dt gives the average velocity of the car.
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