Motion Along a Straight Line

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Chapter-2

• Motion Along a Straight Line

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Ch 2-1 Motion Along a Straight Line

• Motion of an object along a straight line
• Object is point mass
• Motion along a horizontal or vertical or inclined
  (line with finite slope) line
• Motion Change in position
• No change in position, body at rest

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Ch 2-3 Position and Displacement

• Axis are used to define position of an object
• Position of an object defined with respect to
  origin of an axis
• Position x of an object is its distance from the
  origin at any time t
• Displacement ?x, a vector, is change in
  position.
• ?x xf-xi
• When an object changes its position, it has a
  velocity

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Check Point 2-1

• Here are three pairs of initial and final
  positions, respectively along x axis. Which pair
  give a negative displacement?
• a) -3 m, 5 m
• b) -3 m, -7 m
• c) 7 m, -3 m

• Ans
• ?xxf-xi
• a) ?xxf-xi5-(-3)8
• b) ?xxf-xi-7-(-3)-4
• c) ?xxf-xi-3-(7)-10
• Ans b and c

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Ch 2-4 Average Velocity, Average Speed

• Average Velocity vavg ?x/ ?t
• vavg (xf-xi) /(tf-ti)
• Average speed Savg a scalar
• Savg total distance/ total time
• Instantaneous Velocity v
• v lim (?x/ ?t)
• ?t?0
• Position-time graph used to define object
  position at any time t and to calculate its
  velocity
• v is slope of the line on position-time graph

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Check Point 2-3

• The following equations give the position x(t) of
  a particle in four situations ( in each equation
  , x is in meters, t is in seconds, and tgt0)
• 1) x 3t-2
• 2) x-4t2-2
• 3) x-2/t2
• 4) x-2
• a) In which situation velocity v of the particle
  constant?
• b) In which v is in the negative direction?

• Ans vdx/dt
• 1) v3 m/s
• 2) v-8t m/s
• 3) v 2/t3
• 4) v0
• a) 1 and 4
• c) 2 and 3

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Ch 2-6 Acceleration

• When an object changes its velocity, it undergoes
  an acceleration
• Average acceleration aavg
• aavg ?v/ ?t
• (vf-vi) /(tf-ti)
• Instantaneous acceleration a
• a lim (?v/ ?t)
• ?t?0
• dv/dtd2x/dt2
• Velocity-time graph used to define object
  velocity at any time t and calculate its
  acceleration
• a is slope of the line on velocity-time graph

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Ch 2-6 Acceleration

• If the sign of the velocity and acceleration of a
  particle are the same, the speed of particle
  increases.
• If the sign are opposite, the speed decreases.

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Check Point 2-4

• A wombat moves along an x axis. What is the sign
  of its acceleration if it is moving
• a) in the positive direction with increasing
  speed,
• b) in the positive direction with decreasing
  speed
• c) in the negative direction with increasing
  speed,
• d) in the negative direction with decreasing
  speed?

• Ans
• a) plus
• b) minus
• c) minus
• d) plus

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Ch 2-7 Constant Acceleration

• Motion with constant acceleration has
• Variable Slope of position-time graph
• Constant Slope of velocity -time graph
• Zero Slope of acceleration -time graph
• For constant acceleration
• a aavg (vf-vi)/(tf-ti)
• vavg (vfvi)/2

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Equations for Motion with Constant Acceleration

• vv0at
• x-x0v0t(at2)/2
• v2v022a(x-x0)
• x-x0t(vv0)/2
• x-x0 vt-(at2)/2

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Check Point 2-5

• The following equations give the position x(t) of
  a particle in four situations
• 1) x3t-4
• 2) x-5t34t26
• 3) x2/t2-4/t
• 4) x5t2-3
• To which of these situations do the equations of
  Table 2-1 apply?

• Ans Table 2-1 deals with constant acceleration
  case hence calculate acceleration for each
  equation
• 1) a d2x/dt20
• 2) a d2x/dt2-30t8
• 3) a d2x/dt2 12/t4-8/t2
• 4) a d2x/dt2 10
• Ans 1 and 4 ( constant acceleration case)

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Ch 2-9 Free Fall Acceleration

• Free fall acceleration g dde to gravity
• g directed downward towards Earths center along
  negative y-axis
• with a -g -9.8 m/s2
• equations of motion with constant acceleration
  are valid for free fall motion

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Check Point 2-6

• (a) plus (upward displacement on y axis)
• (b) minus (downward displacement on y axis)
• (c) a -g -9.8m/s2

• What is the sign of the balls displacement for
  the ascent, from the release point to the highest
  point?
• B) What is it for the descent , from the highest
  point back to to the release point
• c) What is the balls acceleration at its highest
  point?

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Ch 2-10 Graphical Integration in Motion Analysis

• Integration of v-t graph to obtain displacement
  ?x ?x x-x0vt ?v dt
• but
• ?v dt area between velocity curve and time
  axis from t0 to t
• Integration of a-t graph to obtain velocity ?v
  Similarly ?v v-v0 ?a dt
• ?a dt area between acceleration curve and
  time axis from t0 to t