Motion Along a Line

3 Key excerpts on "Motion Along a Line"

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  eBook - ePub

  Biomechanics For Dummies

  • Steve McCaw(Author)
  • 2014(Publication Date)
  • For Dummies

    (Publisher)

  translation. In linear motion, all points on a body go equally far in the same direction, they travel equally fast, and they move at the same time. All points on the body also speed up and slow down at the same time. There are two forms of linear motion:

  • Rectilinear motion: Motion in a straight line.
  • Curvilinear motion: Motion along a curved line, such as when a body moves through the air as a projectile. Curvilinear motion is simultaneous motion in the up–down (vertical) and forward–backward (horizontal) directions.

  In this chapter, I explain the kinematic descriptors to describe where a body is in space (position) and how far, how fast, and how consistently (speeding up or slowing down) the body moves. I introduce the important quantity of linear momentum because it combines the two critical ideas of the body's current state of motion and the body's resistance, or inertia, to changing its motion. Finally, I demonstrate the use of the three equations of constant acceleration to quantify projectile motion.

  Identifying Position

  Position describes a body's location in space. The location is specified relative to a selected landmark. The landmark is referred to as the origin, because all measures of position are made from, or originate from, this point. Figure 5-1 shows a view from above of a player on a soccer field (or pitch, to be sport-term correct) at a specific instant in time. I've set the origin to a coordinate system (see Chapter 2 ) where the goal line and the sideline meet in the bottom-left corner of the field; the x direction corresponds to the length of the field, and the y

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  eBook - ePub

  Foundations of Mechanical Engineering

  • A. D. Johnson(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  Motion of bodies 2

  2.1 Aims

  • To introduce the concepts of linear and angular motion.
  • To explain the relationships between displacement, velocity and acceleration.
  • To explain the relationship between absolute and relative velocities.
  • To define the equations used to analyse linear and angular motion.
  • To introduce an approach by which linear and angular motion problems can be analysed.
  • To explain related topics such as ‘falling bodies’, ‘trajectories’ and vector methods.

  2.2 Introduction to Motion

  When traffic lights turn to green a car will move away with increasing velocity. The car will cover a distance in a particular direction and will possess a particular velocity at any instant. During this process the car possesses the three basic constituents of motion, namely: displacement, velocity and acceleration. It should be noted that since the car runs on wheels, these will also be in motion and therefore possess displacement, velocity and acceleration. However, the car moves in a linear direction, while the wheels move in an angular direction.

  2.2.1 Displacement

  If a man walks 10 km, there is an indication of the distance between the start position and the final position, but there is no indication of the direction. The 10 km is merely the distance covered and, as such, is a scalar quantity, i.e. possessing magnitude only. Displacement, however, implies a change in position or movement over a distance and gives the position and direction from the start point. Thus displacement is a vector quantity possessing both magnitude and direction.

  Fig. 2.1 Displacement diagram.

  Figure 2.1 gives an example of a man who walks 3 km east then 4 km north. He has actually walked a distance of 7 km but has been displaced from his start point by only 5 km.

  2.2.2 Velocity

  Velocity is the value of displacement measured over a period of time. It is the rate over which a distance/displacement is traversed. The magnitude of velocity is often expressed in convenient units such as kilometres per hour or miles per hour; however, these should be regarded as observation and comparison units. For analysis purposes velocity is better expressed in SI units of m/s.

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  eBook - ePub

  Understanding Physics

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

    (Publisher)

  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 (b)), demonstrates this point.

  Figure 4.16

  (a) The change in velocity of a point as it moves from A to B. (b) The direction of the change in velocity of a point as it moves from A to B in is determined by the triangle rule for vector addition. The direction of the acceleration is parallel to Δv in the limit Δt → 0.

  Linear motion, in which displacement, velocity and acceleration are all directed along the same straight line, is a special case. Equations equivalent to those used in Section 2.5 to describe the special cases of constant velocity and constant acceleration in one dimension can be written in vector form by replacing the algebraic quantities x, v and a, respectively, by their vector equivalents r, v and a. Equation (2.14) for constant velocity becomes

  (4.1)

  This equation describes motion in a straight line with constant (vector) velocity as illustrated in Figure 4.17 .

  Figure 4.17

  Motion with constant velocity. If the displacement of the moving point at t = 0 is r0 , its displacement at any other time t is given by Equation (4.1) .

  For motion with constant acceleration, where the origins of coordinates and time are chosen such that r0 = 0 and t0 = 0,

  (4.2a)

  (4.2b)

  Equation (4.2a) is represented as a vector addition triangle in Figure 4.18 .

  Figure 4.18

  Motion with constant acceleration A. The velocity v of the moving point at time t is given by Equation (4.2a) , where v0 is its velocity at t

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