Equations involving Constant Acceleration

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Equations involving Constant AccelerationWorkin
g with Kinematics Graphs

• Physics 11

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Kinematics Equations for Constant Acceleration

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Sample Problem

• If a rocket with an initial velocity of 8.0 m/s
  at t 0 s accelerates at a rate of 10.0
  m/s2 for 2.0 s, what is its final velocity at
  t 2.0 s ?

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Kinematics Equations for Constant Acceleration

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Sample Problem

• What is the displacement of a bullet train as it
  is accelerated uniformly from 15 m/s to 35 m/s
  in a 25 s time interval?

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Kinematics Equations for Constant Acceleration

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N.B. If an object starts from rest, then vi 0
m/s and d ½ at2 (i.e. this d-t graph looks
like a parabola)
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Sample Problem

• A car starting from rest accelerates uniformly at
  7.2 m/s for 8.0 s. How far does the car move?

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Kinematics Equations for Constant Acceleration

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Note this equation does not involve time !
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Sample Problem

• An airplane must reach 75 m/s for take-off. If
  the runway is 0.5 km long, what must the constant
  acceleration be?

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Acceleration due to Gravity

• "g" is a vector quantity
• -g -9.81 m/s 2 (an average value across Earth)
• N.B. neglect air resistance
• g can be substituted in equations for constant
  acceleration previously in notes

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Sample Problem

• A 3.0-kg stone is dropped for a height of 5.0 m.
  How long does it take to reach the ground? What
  is its velocity at the moment it hits the ground?

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From Position-Time to Velocity-Time to
Acceleration-Time

• We have seen that we can use slopes (whether from
  constant or instantaneous velocity) from a
  position-time graph to find information to draw a
  velocity-time graph
• Further, we have seen that using slopes from a
  velocity-time graph will provide information to
  draw an acceleration-time graph

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From Acceleration-Time to Position-Time

• A car accelerates at a constant 0.75m/s2 plot an
  acceleration-time graph to represent this
  situation (showing time to 10 seconds)
• On the graph, calculate the area under the curve
  for the following times
• 0s-2.5s
• 0s-5s
• 0s-7.5s
• 0-s-10s
• What are the units of the area? What does this
  mean?

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From Acceleration-Time to Position-Time
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From Acceleration-Time to Position-Time

• Use the velocity data from the previous question
  (area under the curve) to plot a velocity time
  graph.
• From the velocity time graph, calculate the area
  under the curve for the following time intervals
• 0s-2.5s
• 0s-5s
• 0s-7.5s
• 0s-10s
• What are the units of the area? What does this
  mean?

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From Acceleration-Time to Position-Time
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From Acceleration-Time to Position-Time

• Use the displacement information from the
  previous question (area under the curve) plot a
  displacementtime graph

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From Acceleration-Time to Position-Time
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Acceleration-Time Graph
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Velocity-Time Graph
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Position-Time Graph
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Equations of Motion