Chapter 2: Motion along a Straight Line

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Chapter 2 Motion along a Straight Line
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Displacement, Time, Velocity
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One-Dimensional Motion

• The area of physics that we focus on is called
  mechanics the study of the relationships between
  force, matter and motion
• For now we focus on kinematics the language used
  to describe motion
• Later we will study dynamics the relationship
  between motion and its causes (forces)
• Simplest kind of motion 1-D motion (along a
  straight line)
• A particle is a model of moving body in absence
  of effects such as change of shape and rotation
• Velocity and acceleration are physical quantities
  to describe the motion of particle
• Velocity and acceleration are vectors

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Position and Displacement

• Motion is purely translational, when there is no
  rotation involved. Any object that is undergoing
  purely translational motion can be described as a
  point particle (an object with no size).
• The position of a particle is a vector that
  points from the origin of a coordinate system to
  the location of the particle
• The displacement of a particle over a given time
  interval is a vector that points from its initial
  position to its final position. It is the change
  in position of the particle.
• To study the motion, we need coordinate system

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Position and Displacement

• Motion of the particle on the dragster can be
  described in terms of the change in particles
  position over time interval
• Displacement of particle is a vector pointing
  from P1 to P2 along the x-axis

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Average Velocity

• Average velocity during this time interval is a
  vector quantity whose x-component is the change
  in x divided by the time interval

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Average Velocity

• Average velocity is positive when during the time
  interval coordinate x increased and particle
  moved in the positive direction
• If particle moves in negative x-direction during
  time interval, average velocity is negative

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X-t Graph

• This graph is pictorial way to represent how
  particle position changes in time
• Average velocity depends only on total
  displacement ?x, not on the details of what
  happens during time interval ?t
• The average speed of a particle is scalar
  quantity that is equal to the total distance
  traveled divided by the total time elapsed.

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Average Velocity
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Instantaneous Velocity

• Instantaneous velocity of a particle is a vector
  equal to the limit of the average velocity as the
  time interval approaches zero. It equals the
  instantaneous rate of change of position with
  respect to time.

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Instantaneous Velocity

• On a graph of position as a function of time for
  one-dimensional motion, the instantaneous
  velocity at a point is equal to the slope of the
  tangent to the curve at that point.

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Instantaneous Velocity
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Instantaneous Velocity

• Concept QuestionThe graph shows position versus
  time for a particle undergoing 1-D motion.
• At which point(s) is the velocity vx positive?
• At which point(s) is the velocity negative?
• At which point(s) is the velocity zero?
• At which point is speed the greatest?

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Acceleration
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Acceleration

• If the velocity of an object is changing with
  time, then the object is undergoing an
  acceleration.
• Acceleration is a measure of the rate of change
  of velocity with respect to time.
• Acceleration is a vector quantity.
• In straight-line motion its only non-zero
  component is along the axis along which the
  motion takes place.

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Average Acceleration

• Average Acceleration over a given time interval
  is defined as the change in velocity divided by
  the change in time.
• In SI units acceleration has units of m/s2.

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Instantaneous Acceleration

• Instantaneous acceleration of an object is
  obtained by letting the time interval in the
  above definition of average acceleration become
  very small. Specifically, the instantaneous
  acceleration is the limit of the average
  acceleration as the time interval approaches zero

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Acceleration of Graphs
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Acceleration of Graphs
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Acceleration of Graphs
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Constant Acceleration Motion

• In the special case of constant acceleration
• the velocity will be a linear function of time,
  and
• the position will be a quadratic function of
  time.
• For this type of motion, the relationships
  between position, velocity and acceleration take
  on the simple forms

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Constant Acceleration Motion
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Constant Acceleration Motion
Position of a particle moving with constant
acceleration
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Constant Acceleration Motion

• Relationship between position of a particle
  moving with constant acceleration, and velocity
  and acceleration itself

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Freely Falling Bodies
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Freely Falling Bodies

• Example of motion with constant acceleration is
  acceleration of a body falling under influence of
  the earths gravitation
• All bodies at a particular location fall with the
  same downward acceleration, regardless of their
  size and weight
• Idealized motion free fall we neglect earth
  rotation, decrease of acceleration with
  decreasing altitude, air effects

Aristotle    384 - 322 B.C.E.
Galileo Galilei 1564 - 1642
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Freely Falling Bodies

• The constant acceleration of a freely falling
  body is called acceleration due to gravity, g
• Approximate value near earths surface g 9.8
  m/s2 980 cm/s2 32 ft/s2
• g is the magnitude of a vector, it is always
  positive number
• Exact g value varies with location

• Acceleration due to gravity
• Near the sun 270 m/s2
• Near the moon 1.6 m/s2