Physics
Velocity
Velocity is a vector quantity that describes the rate and direction of an object's motion. It is calculated as the displacement of an object per unit of time and is typically measured in meters per second (m/s) or kilometers per hour (km/h). In essence, velocity indicates both how fast and in which direction an object is moving.
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12 Key excerpts on "Velocity"
eBook - PDFGeneral Engineering Science in SI Units
The Commonwealth and International Library: Mechanical Engineering Division
- G. W. Marr, N. Hiller(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
Section 2 Velocity and Acceleration 2.1. Motion When the position of one body relative to another is continuously changing the bodies are said to be in relative motion. Motion, in fact, is always relative. In very many cases we are concerned with the motion of a body relative to the earth, and in such cases the word relative is generally omitted. We are accustomed to refer-ring simply to the motion of a motor vehicle or aircraft. We may say, for example, that a caj* is travelling at a speed of 30 km/h. When we do so, it must be understood that the speed is relative to the earth. 2.2. Velocity The Velocity of a body is the rate at which the body is changing its position. Because direction is involved, Velocity is a vector quantity. The magnitude, or numerical value, of a Velocity is called the speed. The average speed of a body during a given interval of time IS measured by the ratio total distance^raven.d in given time W h e n a body travels equal distances during equal intervals of time, what-ever the magnitude of the time interval, the body is said to travel with constant speed. A Velocity may change because of change in speed, or in the direction of motion or because of a change v in both of these. 32 Velocity AND ACCELERATION When a body moves in such a way that its Velocity does not change, it is said to move with constant, or uniform, Velocity. Hence to move with uniform Velocity, a body must travel at constant speed in a straight line. EXAMPLE. A vehicle travels a distance of 840 m in 30 sec. Express its average speed in km/h. Distance travelled = 840 m = 0-84 km. 30 s = ai 0-84 km Time interval = 30s = g§öö h = iiö-h .*. average speed — —j = 100-8 km/h. EXAMPLE. The straight-line distance between two towns, A and B, is 49 km. Town A is due north-west from B. The road distance between the towns is 56 km. A motorist leaves A at 13.20 h and arrives at B at 14.10 h. Calculate (a) his average speed; (b) his average Velocity.
eBook - PDFGeneral Engineering Science in SI Units
In Two Volumes
- G. W. Marr, N. Hiller(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
Section 2 Velocity and Acceleration 2.1. Motion When the position of one body relative to another is continuously changing the bodies are said to be in relative motion. Motion, in fact, is always relative. In very many cases we are concerned with the motion of a body relative to the earth, and in such cases the word relative is generally omitted. We are accustomed to refer-ring simply to the motion of a motor vehicle or aircraft. We may say, for example, that a car is travelling at a speed of 30 km/h. When we do so, it must be understood that the speed is relative to the earth. 2.2. Velocity The Velocity of a body is the rate at which the body is changing its position. Because direction is involved, Velocity is a vector quantity. The magnitude, or numerical value, of a Velocity is called the speed. The average speed of a body during a given interval of time is measured by the ratio total distance um^d m given time w h e n a body travels equal distances during equal intervals of time, what-ever the magnitude of the time interval, the body is said to travel with constant speed. A Velocity may change because of change in speed, or in the direction of motion or because of a change in both of these. 32 Velocity AND ACCELERATION When a body moves in such a way that its Velocity does not change, it is said to move with constant, or uniform, Velocity. Hence to move with uniform Velocity, a body must travel at constant speed in a straight line. EXAMPLE. A vehicle travels a distance of 840 m in 30 sec. Express its average speed in km/h. Distance travelled = 840 m = 0-84 km. Time interval = 3 0 s = a|ööh = 1 ^-h 0-84 km .·. average speed = —j I2Ö h = 100-8 km/h. EXAMPLE. The straight-line distance between two towns, A and B, is 49 km. Town A is due north-west from B. The road distance between the towns is 56 km. A motorist leaves A at 13.20 h and arrives at B at 14.10 h. Calculate (a) his average speed; (b) his average Velocity.
eBook - PDF- James Shipman, Jerry Wilson, Charles Higgins, Bo Lou, James Shipman(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
● ● Motion involves a continuous change of position. 2.2 Speed and Velocity Key Questions ● ● Between two points, which may be greater in magnitude, distance or displacement? ● ● What is the difference between speed and Velocity? The terms speed and Velocity are often used interchangeably; however, in physical sci- ence, they have different distinct meanings. Speed is a scalar quantity, and Velocity is a vector quantity. Let’s distinguish between scalars and vectors now, because other terms will fall into these categories during the course of our study. The distinction is simple. A scalar has only magnitude (numerical value and unit of measurement). For example, you may be traveling in a car at 90 km/h (about 55 km/h). Your speed is a scalar quan- tity; the magnitude has the numerical value of 90 and unit of measurement km/h. A vector has magnitude and direction. For example, suppose you are traveling at 90 km/h north. This describes your Velocity, which is a vector quantity because it consists of mag- nitude plus direction. By including direction, a vector quantity gives more information than a scalar quantity. No direction is associated with a scalar quantity. Vectors may be graphically represented by arrows. The length of a vector arrow is proportional to the magnitude and may be drawn to scale. The arrowhead indicates the direction of the vector (●●Fig. 2.2). Notice in Fig. 2.2 that the red car has a negative Velocity vector, 2v c , that is equal in magnitude (length of arrow) but opposite in direction, to the positive Velocity vector, +v c , for the blue car. The Velocity vector for the man, v m , is shorter than the vectors for the cars because he is moving more slowly in the positive (1) direction. (The 1 sign is often omitted as being understood.) Speed Now let’s look more closely at speed and Velocity, which are basic quantities used in the description of motion.
- Paul Anthony Russell(Author)
- 2021(Publication Date)
- Reeds(Publisher)
Kinematics is about the study of motion in the real world without considering the size or shape of machines or objects or the forces that cause the motion. Linear Motion SPEED is the rate at which a body moves through space; however, speed does not define the direction of a moving body and is, therefore, expressed as the distance travelled in a given time. The units of speed are metres per second (ms −1 ), kilometres per hour (km/h), etc. Speed may also change during a journey; for example, if a car covers180 km in 3 h, it is very improbable that it has been moving at a constant speed of 60 km/h, but the average is 60 km/h. Therefore, speed is described as a scalar quantity, as only one fact about the body is defined. Velocity, however, indicates speed in a specified direction. Velocity represents two facts about a moving body – its speed and also its direction; consequently, Velocity is a vector quantity and hence can be illustrated by drawing an arrow (vextor) to scale, the length of which represents the speed of the body and the arrowhead on it represents its direction. See Figure 2.1. RESULTANT Velocity is obtained from vector diagrams of velocities in the same manner as with vector diagrams of forces. Resultant Velocity is an outcome of vector addition. KINEMATICS 2 N S W E 2 m/s due east 18 km/h south-west ▲ Figure 2.1 Vectors showing Velocity Example 2.1. A ship travelling due north at 16 knots runs into a 4-knot current moving south-east. Find the resultant speed and direction of the ship. ( ) ( ) ( ) cos cos ac ab bc ab bc b 2 2 2 2 2 2 16 4 2 16 4 45 256 16 = + - × × × = + - × × × ° = + - = = = ° = × = 90 51 181 49 13 47 4 13 47 45 4 0 7071 13 47 . . . sin . sin sin . . ac a a 0 2100 12 7 . ∴ = ° ′ a ∴ = = ° ′ resultant speed knots resultant direction east of 13 47 12 7 . north A CHANGE OF Velocity will take place if speed changes, or if direction changes, or if both speed and direction change.
eBook - PDF- Vern Ostdiek, Donald Bord(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
(d) can be perpendicular to one of the original velocities. ANSWERS: 1. (c) 2. (a) 3. vector 4. False 5. (b) 1.3 Acceleration The physical world around us is filled with motion. But think about this for a moment: cars, bicycles, pedestrians, airplanes, trains, and other vehicles all change their speed or direction often. They start, stop, speed up, slow down, and make turns. The Velocity of the wind usually changes from moment to mo- ment. Even Earth as it moves around the Sun is constantly changing its direc- tion of motion and its speed, though not by much as reckoned on a daily basis. The main thrust of Chapter 2 is to show how the change in Velocity of an object is related to the force acting on it. For these reasons, a very important concept in physics is acceleration. Physical Quantity Metric Units English Units Acceleration ( a ) meter per second 2 (m/s 2 ) foot per second 2 (ft/s 2 ) mph per second (mph/s) Whenever something is speeding up or slowing down, it is undergoing accel- eration. As you travel in a car, anytime the speedometer’s reading is changing, the car is accelerating. Acceleration is a vector quantity, which means it has both magnitude and direction. Note that the relationship between acceleration and Velocity is the same as the relationship between Velocity and displacement. Acceleration indicates how rapidly Velocity is changing, and Velocity indicates how rapidly displacement is changing. EXAMPLE 1.3 A car accelerates from 20 to 25 m/s in 4 seconds as it passes a truck (Figure 1.15). What is its acceleration? Acceleration Rate of change of Velocity. The change in Velocity divided by the time elapsed. a 5 D v D t DEFINITION Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 26 Chapter 1 The Study of Motion SOLUTION Because the direction of motion is constant, the change in Velocity is just the change in speed—the later speed minus the earlier speed.
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Hence- forth, when we refer to an object’s Velocity, we mean its instantaneous Velocity, with the magnitude of the instantaneous Velocity being the object’s (instantaneous) speed. 2.4 Solve problems involving average acceleration, Velocity, and time. 2.4.1 Interpret or determine the direction of the acceleration. If your friend tells you that her Velocity has changed, what she probably means is that the magnitude of her Velocity has increased or decreased; that is, the speed with which she is moving has changed. Your friend may use the word acceleration or deceleration when speaking about her changing speed. These words have very specific meanings in physics and, like Velocity, the way they are used in everyday conversation is sometimes inconsist- ent with their scientific definitions. When an object’s Velocity changes, we say that there is acceleration. Suppose that the Velocity changes from v 0 to v in a time t t t 0 ∆ = − . We define the object’s average acceler- ation in the following way: a v t v v t t avg 0 0 = ∆ ∆ = − − (2.4.1) The SI unit of acceleration is / m s 2 . Acceleration is a vector quantity, so it has a magni- tude and a direction, with the direction of the acceleration being the same as the direction of the change in Velocity. There is acceleration if there is a change in the direction of the Velocity, in the magnitude of the Velocity (i.e., the speed), or in both. To illustrate the use of Equation 2.4.1, consider the situation depicted in Animated Figure 2.4.1. A rocket, moving in the positive x direction, is coasting in space at a speed 2.4 ACCELERATION Learning Objectives Animated Figure 2.4.1 A rocket fires its forward thrusters and its speed increases. 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 Acceleration | 51 A car is traveling at a speed of 21.8 m/s. The driver taps the brakes for 3.2 s during which time the magnitude of the average acceleration is 1.5 m/s 2 .
eBook - PDFWorkshop Physics Activity Guide Module 1
Mechanics I
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Unless the position graph consists of a single, straight line, the average Velocity between two points will, in general, depend on the points you choose. In addition to the average Velocity, we may also want to know the instanta- neous Velocity, defined as the slope of the line tangent to the graph at a particular time. Mathematically, the instantaneous Velocity is given by the derivative of UNIT 3: INTRODUCTION TO ONE-DIMENSIONAL MOTION 71 the position-time graph (the slope between two points that are infinitely close together): x = lim Δt→0 Δx Δt = dx dt (3.1) The Velocity Vector When dealing with more than one dimension, an object’s position should be considered a vector quantity, r = x x + y y + z z, so it becomes difficult to plot “the position” of an object in two (or three) dimensions. In these cases the concept of the “slope” of the position graph begins to lose its meaning. However, we can still define the average Velocity to be the change in the position vector divided by the change in time: avg ≡ ⟨ ⟩ = Δ r Δt = Δx Δt x + Δy Δt y + Δz Δt z (3.2) where the bracket around denotes the average. When written this way, we see that the vector nature of Velocity is a direct result of the vector nature of position. As you might guess, the instantaneous Velocity vector is defined as the derivative of the position vector with respect to time: = lim Δt→0 Δ r Δt = d r dt = dx dt x + dy dt y + dz dt z = x x + y y + z z (3.3) Stated another way, Velocity is the rate of change of position with respect to time. The instantaneous Velocity vector points in the direction the object is moving at that instant and, as with any vector, the magnitude of the Velocity vector is given by its length, = | | = √ x 2 + y 2 + z 2 . As we saw in Unit 1, a vector can be represented by an arrow (whether in one or more dimensions).
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
Recall that Velocity is a vector—it has both magnitude and direction. This means that a change in Velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when Velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both. Acceleration as a Vector Acceleration is a vector in the same direction as the change in Velocity, Δv . Since Velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both. Keep in mind that although acceleration is in the direction of the change in Velocity, it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration. 40 Chapter 2 | Kinematics This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 Figure 2.13 A subway train in Sao Paulo, Brazil, decelerates as it comes into a station. It is accelerating in a direction opposite to its direction of motion. (credit: Yusuke Kawasaki, Flickr) Misconception Alert: Deceleration vs. Negative Acceleration Deceleration always refers to acceleration in the direction opposite to the direction of the Velocity. Deceleration always reduces speed. Negative acceleration, however, is acceleration in the negative direction in the chosen coordinate system. Negative acceleration may or may not be deceleration, and deceleration may or may not be considered negative acceleration. For example, consider Figure 2.14. Chapter 2 | Kinematics 41 Figure 2.14 (a) This car is speeding up as it moves toward the right. It therefore has positive acceleration in our coordinate system. (b) This car is slowing down as it moves toward the right.
eBook - PDF- John Matolyak, Ajawad Haija(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
27 Motion in One Dimension © 2010 Taylor & Francis Group, LLC The above example presents to us the first case in which we see an important difference between displacement and distance. Displacement, in essence, is a vector quantity that could take positive, negative, or zero values. But distance is always a positive number. 2.2 AVERAGE Velocity The average Velocity of an object moving between two positions in a certain period of time is an abstract quantity that gives an idea of what constant Velocity it would need to travel through the distance separating the two positions in the same period of time. This is an ideal notion, since most motions are not constant in time. However, the concept of the average Velocity as will be seen shortly is very useful. The average Velocity of an object moving between two locations in the time interval, Δ t, is defined as ν = ∆ ∆ ∆ = ∆ = --x t x x x t t t f i f i ; ; (2.2) or ∆ = ∆ x t ν (2.3) or, assuming that the start is set at t i = 0, then ∆ = x t ν . (2.4) This is graphically projected in Figure 2.2 in which point P designates the initial location and point Q designates the final destination. Notice that the curve between points P and Q represents the actual path of the object’s motion. However, the dotted straight line connecting points P and Q is a short-cut path that alternatively tells one if the object was going along this short cut, it would reach its destination Q in the same time interval Δ t that it actually took the object to get to Q. In the x–t plot, Δ x/ Δ t is simply the slope (rise/run) of the dotted, straight line PQ. It should be noted that since Δx in Equation 2.2 is a vector, the average Velocity is a vector and connecting the possible values that Δx could take, the average Velocity of an object during a certain motion could assume positive, negative, or zero values. It is the sign of the displacement Δx that dictates the sign of the average Velocity.
eBook - PDFApplied Mechanics
Made Simple
- George E. Drabble(Author)
- 2013(Publication Date)
- Made Simple(Publisher)
CHAPTER TWO THE NATURE OF MOTION Without concerning ourselves about the reasons why motion takes place (these we shall deal with in Chapter Four), let us consider a familiar case of a moving object: an aircraft crossing the Atlantic. The first consideration is where it is going to and where it has come from. In terms of applied mechanics, we call this the displacement of the aircraft. The second consideration (a very important one) is how long it takes to perform the journey. This is deter-mined by the average rate of travel along the route chosen, and we call this the average Velocity. Thirdly, and finally, we know that, although it is con-venient for our schedules to speak of an average speed of, say 550 miles an hour, under practical conditions the actual speed is bound to vary from this. To take the two most obvious divergencies, the plane cannot start at 550 miles an hour, nor can it finish at this speed. The Velocity, then, has to change from time to time, and the rate at which it does this is termed the acceleration. Let us look at each of these aspects of motion in turn. (1) Displacement Displacement seems to be a very simple concept. But if we are going to deal mathematically with it, which is exactly what the study of applied mechanics purports to do with physical situations, we have to be very careful to make sure that the rules of mathematics work when applied to each and every situation. Let us try to apply a simple mathematical rule of addition to displacement. We know that, mathematically, 2 added to 3 makes 5. This is easy; but implicit in this simple statement are quite a few important conditions. First, the two things added must be of the same kind. Two years added to three months does not add up to five of anything. Secondly, applying the rule to displacement, it seems obvious at first that two feet added to three feet makes five feet; and indeed this is true if, for instance, we are measuring out material or merely measuring distance travelled.
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)
In fact, in the limit that Δt becomes infinitesimally small, the instantaneous Velocity and the average Velocity become equal, so that v = lim Δt→0 Δ x Δt (2.3) The notation lim Δt→0 Δ x Δt means that the ratio Δ x∕Δt is defined by a limiting process in which smaller and smaller values of Δt are used, so small that they approach zero. As smaller values of Δt are used, Δ x also becomes smaller. However, the ratio Δ x∕Δt does not become zero but, rather, approaches the value of the instantaneous Velocity. For brevity, we will use the word Velocity to mean ‘instantaneous Velocity’ and speed to mean ‘instantaneous speed’. 2.3 Acceleration LEARNING OBJECTIVE 2.3 Define one-dimensional acceleration. PHOTO 2.1 As this sprinter explodes out of the starting block, her Velocity is changing, which means that she is accelerating. In a wide range of motions, the Velocity changes from moment to moment, such as in the case of the sprinter in photo 2.1. To describe the manner in which it changes, the concept of acceleration is needed. The veloc- ity of a moving object may change in a num- ber of ways. For example, it may increase, as it does when the driver of a car steps on the gas pedal to pass the car ahead. Or it may decrease, as it does when the driver applies the brakes to stop at a red light. In either case, the change in Velocity may occur over a short or a long time interval. To describe how the Velocity of an object changes during a given time interval, we now introduce the new idea of acceleration. This idea depends on two concepts that we have previously encountered, Velocity and time. Specifically, the notion of acceleration emerges when the change in the Velocity is combined with the time during which the change occurs. The meaning of average acceleration can be illustrated by considering a plane during take-off. Figure 2.4 focuses attention on how the plane’s Velocity changes along the runway.
eBook - PDF- David Agmon, Paul Gluck;;;(Authors)
- 2009(Publication Date)
- WSPC(Publisher)
Chapter 2 Kinematics All is influx, nothing stands still. Heraclitus Kinematics is a part of mechanics dealing with the description of motion and the functional relationships between a body's position, Velocity, acceleration and time. Complex objects like a car or an airplane are treated as if they were a single mass point, called a particle, allowing one to ignore internal motions. This greatly simplifies the description of the position and related quantities. 2.1 Position and displacement Position is specified with respect to some arbitrary coordinate system, the latter always chosen to satisfy the need for convenience and simplicity. It is usual y { to work with three mutually perpendicular (Cartesian) system of axes, x,y£. For motion in a plane or along a line, two axes (x,y) or one axis (usually x) will suffice, respectively. The choice of the origin O is also a matter of convenience. The same spatial point will have different coordinates in different coordinate systems. We shall usually restrict our discussion to motion in a plane, generalization to three dimensions will be simple. The position of a point P with respect to the (x,y)-axes in the diagram may be specified in three different ways: (a) By the pair of numbers (xi,yi)» which represent the projections of the vector r on the x and y axes, respectively. (b) By the pair (r,#), where r is the distance of P from the origin and 6 is the angle between the x-axis and the line OP. (c) By the vector r, with tail at O and tip at P. The dotted line in the diagram is the time-dependent path of a particle. At time t the particle is at P located by the (position) vector /i, at a later time t 2 it is at P 2 given by the vector r 2 . The displacement vector r 2 starts from Pi and ends at P 2 , and is given by r 2 i=r 2 -r 1 as shown. We denote r 21 by Ar . Pi ^21=^2-^1 25
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