Sect. 3-A Position, Velocity, and Acceleration

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Sect. 3-APosition, Velocity, and Acceleration
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• Position function -
• gives the location of an object at time t,
  usually s(t), x(t) or y(t)
• Velocity -
• The rate of change( derivative) of position,
  usually v(t)
• Acceleration -
• The rate of change ( derivative) of velocity
  usually a(t)
• Average velocity -

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• 1) If
• find v(t) and a(t).

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• 2) The position of a particle moving along the x
  - axis at time t is given by
• . Find the
  particles velocity and acceleration at t 5.

Velocity
Acceleration
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• Speed The absolute value of velocity otherwise
  known as the magnitude of velocity

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Velocity

• Positive - the particle is moving to the right
• Negative - the particle is moving to the left
• Zero - the particle has momentarily stopped or is
  changing direction ( must have a sign change)

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• 3) Find where the object changes direction if

Find where v(t) 0
interval
time
V(t)
Result
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Acceleration and Velocity

• If the sign of acceleration is the same as
  velocity, the speed of the particle is
  ______________ (the two are working together)
• If the sign of the acceleration is opposite that
  of velocity, the speed of the particle is
  _________________ (the two are working against
  each other)

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• 4) Given the same position function as 3
• find the interval during which the
  particle is slowing down.

Interval
t
velocity
acceleration
result
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• 5) Given
  find the interval during which the particle is
  speeding up.

Interval
t
velocity
acceleration
result
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Distance vs. Displacement

• Displacement- change in position ( final
  position minus original position)
• Distance- the total distance travelled by an
  object in the time interval even if duplicated

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• 6) Find the DISTANCE traveled by the particle
  whose position is given by
• on the interval (0,4).

Distance NOT displacement!!
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• 7) If
• find the DISTANCE traveled by the particle on the
  interval (2,4).
• Find the DISPLACEMENT on the interval (1,5)

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• The graph shows the position function of a radio
  controlled car
• a) Was the car going faster at B or at C?
• b) When was the car stopped?
• c) At which point was the cars velocity
• the greatest?
• d) At which point was the cars speed
  decreasing?

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Homework

• PVA Worksheet and
• worksheet 3-A