Velocity-Time Graphs

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Velocity-Time Graphs

• SNC2D Physics
• M. M. Couturier

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Velocity-Time Graphs

• As the term suggests, a velocity-time graph is a
  graph where velocity is plotted on the y-axis and
  time is plotted on the x-axis.

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Velocity-Time Graphs

• Since acceleration is related to velocity and
  time (m/s2), the slope of the function will
  reveal the average acceleration.

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Velocity-Time Graphs

• As we did with position-time graphs, we need to
  understand the nature of the acceleration so we
  must understand all four kinds of slopes
  increasing, decreasing, and zero (within this new
  context).

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Velocity-Time Graphs

• This is an example of a zero slope. The change
  in velocity here is ?v 0 over a period of time,
  t. The average acceleration is therefore
• aavg ?v 0 0
• ?t t
• Essentially, the object is traveling at a
  constant velocity.

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Velocity-Time Graphs

• This is an example of an increasing slope. ?v
  and ?t are both positive and therefore, aavg will
  also be positive. Also, since it is a straight
  line (linear), the acceleration is constant,
  meaning the acceleration is the same.

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Velocity-Time Graphs

• This is an example of a decreasing slope. ?v is
  negative and since ?t can only be positive, aavg
  will be negative. They are slowing down.

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Velocity-Time Graphs

• Use this as an easy reference guide!!!

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Velocity-Time Graphs

• Use this as an easy reference guide!!!

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Velocity-Time Graphs

• In order to calculate the average acceleration
  using a velocity-time graph, you need to isolate
  two points on a single line. Look at the
  velocity-time graph below and write down the
  coordinates of any two points on the line.

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Velocity-Time Graphs

• Since the average acceleration is defined by
• aavg ?v
• ?t
• The two points that we have selected provide both
  ?v and ?t.

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Velocity-Time Graphs

• Lets say that you selected (t,v) as (4,8) and
  (0,0). Your ?v (8-0) and your ?t (4-0),
  hence
• aavg ?v (8 0) 8
• ?t (4-0) 4
• aavg 2 m/s
• Does it matter which
• point you choose?

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Velocity-Time Graphs

• Lets say that you selected (t,v) as (2,4) and
  (1,2). Your ?v (4-2) and your ?t (2-1),
  hence
• aavg ?v (4 2) 2
• ?t (2-1) 1
• aavg 2 m/s
• Does it matter which
• point you choose? It does not matter!!!

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Velocity-Time Graphs

• Again, never hesitate to draw on the graph that
  is provided to you in the following manner.

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Velocity-Time Graphs

• Okay lets describe qualitatively what is
  happening in each of these situations.

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Velocity-Time Graphs

• Red car Notice that the red car is moving at a
  constant velocity. It is therefore not
  accelerating.

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Velocity-Time Graphs

• Green car Notice that the green car is
  increasing in velocity and is therefore
  accelerating. It is taking much more time to
  accelerate than the blue car, but it will
  eventually pass the red car.

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Velocity-Time Graphs

• Blue car The blue car is also increasing in
  velocity and is therefore accelerating. It is
  accelerating at a faster rate than the green car.
  

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Review of position-time graphs

• Which graph goes with which car?

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Review of position-time graphs

• Which graph goes with which car?

• B
• C
• A

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Lets bring it all together!!!

• Watch the graphs and the cars!!!

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Lets bring it all together!!!
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Lets bring it all together!!!

• The blue dot is being displaced equally each unit
  of time ergo it is moving at a constant
  velocity, ergo, it is not accelerating!

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Lets bring it all together!!!
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Lets bring it all together!!!

• The blue dot is being displaced equally each unit
  of time ergo it is moving at a constant
  velocity, ergo, it is not accelerating!

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Lets bring it all together!!!
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Lets bring it all together!!!

• The displacement of the blue dot is larger after
  each unit of time. It is therefore increasing in
  velocity, which is increasing equally each unit
  of time ergo it is accelerating at a constant
  rate.

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Lets bring it all together!!!
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Lets bring it all together!!!

• The displacement of the blue dot is smaller after
  each unit of time. It is therefore decreasing in
  velocity, which is decreasing equally each unit
  of time ergo it is accelerating at a negative
  constant rate.

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Velocity-Time Graphs

• Task 1 Look at the graph below and determine
  the aaverage in each case and then write a short
  story to explain the events. Be creative.

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Velocity-Time Graphs

• Task 2 Look at the graph below and determine
  the aaverage in each case and then write a short
  story to explain the events. Be creative.

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Velocity-Time Graphs

• Lets do a test
• http//www.explorelearning.com/index.cfm?methodcR
  esource.dspViewResourceID301