Acceleration

4 Key excerpts on "Acceleration"

• 

  eBook - ePub

  Describing Motion

  The Physical World

  • Robert Lambourne(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Acceleration is a key idea in physics. It was Newton’s recognition of the crucial role that Acceleration played in determining the link between motion and force that formed the centrepiece of the Newtonian revolution. The detailed study of that revolution would take us too far from our present theme. For the moment let’s concentrate on some basic questions about Acceleration itself. In particular, in what units should Acceleration be measured, and what are typical values of Acceleration in various physical contexts? The first of these you can answer for yourself.

  • What are suitable SI units for the measurement of Acceleration?
  • O Since Acceleration is the rate of change of velocity with respect to time, the units of Acceleration are the units of velocity (ms–1 ) divided by the units of time (s), so Acceleration is measured in metres per second per second, which is abbreviated to ms–2 . ■

  As for typical values of Acceleration, some physically interesting values are shown in Figure 1.25 .

  Figure 1.25 Some physically interesting values of Acceleration.

  When dealing with non-uniform motion along the

  x -axis

  , the symbol

  ax (t)

  is normally used to denote instantaneous Acceleration. As usual,

  ax (t)

  will be positive if the velocity is increasing with time, though, as you will see below, this statement needs careful interpretation. In contrast to the relationship between velocity and speed, there is no special name for the magnitude of an Acceleration, though we shall use the symbol a (t ) for this quantity, so we may write

  a ( t ) = |

  a x

  ( t ) | . (1.12)

  In physics, the concept of Acceleration is precise and quantitative. It is important to realize that this precise definition differs, in some respects, from everyday usage. In ordinary speech, ‘accelerating’ is a synonym for ‘speeding up’. This is not true in physics. In physics, a particle accelerates if it changes its velocity in any way. A particle travelling along a straight line may accelerate by speeding up or

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  eBook - ePub

  BIOS Instant Notes in Sport and Exercise Biomechanics

  • Paul Grimshaw, Neil Fowler, Adrian Lees, Adrian Burden(Authors)
  • 2007(Publication Date)
  • Routledge

    (Publisher)

  This is assuming that the effect of air resistance (see section D), is negligible; which it can be for bodies of large mass traveling at low speeds. The Acceleration that a body experiences as a consequence of the gravitational force varies slightly depending on its position on Earth (it is slightly greater at the poles than the equator) but is generally agreed to be equal to 9.81 m·sec −2. It should also be referred to as negative (i.e., −9.81 m·sec −2) because the Acceleration acts in a downwards direction, towards the surface of the Earth. However, other constant Acceleration situations can occur when a body is not airborne. For example, a cyclist who stopped pedaling on a flat road would experience a fairly constant horizontal deceleration. Similarly, providing it was traveling up or down a smooth incline, a bobsleigh would also experience an approximately constant deceleration or Acceleration. Effects of constant Acceleration When a body is moving in one direction in a straight line under constant Acceleration (e.g., a car experiencing approximately constant Acceleration at the start of a race) its velocity increases in a linear fashion with respect to time and thus its position changes in a curvilinear (exponential) manner, as shown in Fig. A7.1. The situation is more complicated when a body moves in two directions, again in a straight line. An example of this is when someone jumps directly up and then lands back in the same place (e.g., a SVJ), and experiences the constant Acceleration due to gravity during both the ascent and descent. In this situation the velocity of the body decreases linearly to zero at the apex of the jump and then increases in the same manner until landing. Their position changes in a curvilinear fashion, as shown in Fig. A7.2. Equations of uniformly accelerated motion The changes in position and velocity of a constantly accelerating body were first noted by an Italian mathematician called Galileo in the early 17th century

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  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Section A.13 .

  Study Appendix A, Section A.11.1 ‐ 6 and Worked Example 4.1

  For problems based on the material presented in this section visit up.ucc.ie/4/ and follow the link to the problems.

  4.3 Velocity and Acceleration vectors

  Velocity

  Consider a point P which is moving in two dimensions (the plane of the page). As indicated in Figure 4.15 , the displacements of P from O at two points A and B on the path of P and the corresponding times are (r, t) and (r + Δr, t + Δt), respectively.

  Figure 4.15

  A point moves from A to B in a time Δt; its change of displacement during that time interval is Δr.

  We can now define velocity in vector form (recall Equation (2.5) for the one‐dimensional version). The velocity of the point P at the instant it is at A is defined as follows

  The quantity is a vector (Δr) multiplied by a scalar ( ) and hence v is a vector in the direction of Δr in the limit Δr → 0, that is in the direction of the tangent to the path at A. Thus the direction of the velocity vector is always tangential to the path of the moving point.

  The magnitude of the velocity vector, denoted by |v|, is called the speed. This is the only case in physics in which the magnitude of a vector is given a special name. Note that if an object is moving at constant speed but changes direction, for example from 30 km per hour due North to 30 km per hour due East, its velocity has changed although its speed has not.

  Acceleration

  In a similar way can define Acceleration in vector form. As illustrated in Figure 4.16 , if the velocities and corresponding times at two points A and B along a point's path of motion are (v, t) and (v + Δv, t + Δt), respectively, the Acceleration of the moving point at A at the instant t is defined as

  Note that the direction of a is in the direction defined by Δv in the limit Δt → 0, which in general is not the same direction as that of v. The velocity vector triangle, representing the addition (v+Δv) = v + Δv (Figure 4.16

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  eBook - ePub

  Superstrings and Other Things

  A Guide to Physics

  • Carlos I. Calle(Author)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  If you are traveling on an airplane, the book you might be reading is at rest with respect to you, but is traveling, along with the other passengers and the entire contents of the plane, at the cruising speed of the plane, about 1000 km/h with respect to the ground. A flight attendant walking up the aisle at 2 km/h with respect to the plane would be moving at 1002 km/h with respect to the ground. Whether an object is at rest or moving with a constant velocity depends on the frame of reference to which it is referred. These special reference frames, in which the law of inertia is valid, are called inertial frames of reference. Thus, motion is entirely relative, an idea that is central to Newton’s laws and was recognized by Newton himself. Newton’s Second Law: The Law of Force Newton’s first law tells us what happens to an object in the absence of a net force. What happens if the net force acting on an object is not zero? According to the first law, the object will not move with a constant velocity. This means, of course, that the object will experience Acceleration in the direction of the applied net force. Newton explained it in Book One of the Principia : Law II: The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. Newton (1687; reprint 1999, p. 416) According to Newton’s second law, when an instantaneous force acts on a body, as when a baseball bat strikes a ball, a change in the body’s motion takes place, which is proportional to the “force impressed.” If the force acts on the body continuously rather than instantaneously, as when we push on an object for some time, Acceleration is produced that is proportional to the applied force. As an illustration of the second law, suppose that your sports car has stalled and you decide to push it (Figure 3.8a). If your car has a mass m of 1000 kg, you would apply a force F for 10 s to accelerate it from rest to a speed of 5 km/h

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