Lesson 7 Acceleration

C7.9 graph paper

You have learned about position-time and velocity-time graphs: how to plot the data to create them, how to find the slope of them, how to find the area under the line of them, and how to interpret them to understand an object’s motion. That is a lot of information to understand and remember. Let’s summarize all of this information.

Summary of Types of Graphs

	Position-Time Graph	Velocity-Time Graph
Stationary Object	C7.10 Position-Time graph of stationary object Position does not change as time passes.	C7.11 Velocity-Time graph of stationary object Velocity is zero as time increases.
Uniform Motion	C7.12 Position-Time graph of uniform motion Position increases the same amount with each time interval. Slope of line is «math» «mover» «mi»v«/mi» «mo»§#8594;«/mo» «/mover» «mo»=«/mo» «mfrac» «mrow» «mo»§#8710;«/mo» «mover» «mi»d«/mi» «mo»§#8594;«/mo» «/mover» «/mrow» «mrow» «mo»§#8710;«/mo» «mi»t«/mi» «/mrow» «/mfrac» «/math».	C7.13 Velocity-Time graph of uniform motion Velocity does not change. Area under graph represents displacement «math» «mfenced» «mrow» «mover» «mi»d«/mi» «mo»§#8594;«/mo» «/mover» «mo»=«/mo» «mo»§#8710;«/mo» «mover» «mi»v«/mi» «mo»§#8594;«/mo» «/mover» «mo»§#8710;«/mo» «mi»t«/mi» «/mrow» «/mfenced» «/math»
Motion with Constant Acceleration	C7.14 Position-Time graph of constant acceleration Position increases a greater amount with each time interval.	C7.15 Velocity-Time graph of constant acceleration Velocity increases the same amount each time interval. Slope of line is «math» «mover» «mi»a«/mi» «mo»§#8594;«/mo» «/mover» «mo»=«/mo» «mfrac» «mrow» «mo»§#8710;«/mo» «mover» «mi»v«/mi» «mo»§#8594;«/mo» «/mover» «/mrow» «mrow» «mo»§#8710;«/mo» «mi»t«/mi» «/mrow» «/mfrac» «/math». Area under graph represents displacement «math» «mfenced» «mrow» «mover» «mi»d«/mi» «mo»§#8594;«/mo» «/mover» «mo»=«/mo» «mfrac» «mrow» «mo»§#8710;«/mo» «mover» «mi»v«/mi» «mo»§#8594;«/mo» «/mover» «mo»§#8710;«/mo» «mi»t«/mi» «/mrow» «mn»2«/mn» «/mfrac» «/mrow» «/mfenced» «/math».

Position-Time Graphs

• If the line on a position-time graph is straight (constant slope) then the object is moving with a constant speed.
• If the line curves to become steeper and steeper over the time interval, then the object is speeding up.
• If the line curves to become less and less steep over the time interval, then the object is slowing down.
• The direction that the line slopes - either upward or downward - indicates whether the velocity is positive (for upward slope) or negative (for downward slope).

Velocity-Time Graphs

• Horizontal lines represent constant-speed motion.
• Diagonal lines represent changing-speed motions.
• If the diagonal line approaches the time axis, then the motion is a slowing-down motion.
• If the diagonal line gets farther from the time axis, then the motion is a speeding-up motion.

1. Use the graph provided to answer the following questions.
   The motion of several objects is depicted on the position-time graph. Each question may have none, one, or more than one answer. Each letter can be used more than once.
   
   
   
   

   

   C7.16 Position-Time graph of several objects

   
   
   
   
   1. Which object(s) is/are at rest?
      
      
      Check your work.
      

      A and E
      
   2. Which object(s) is/are accelerating?
      
      
      Check your work.
      

      D
   3. Which object(s) is/are not moving?
      
      
      Check your work.
      

      A and E
      
   4. Which object(s) change(s) its direction?
      
      
      Check your work.
      

      none
   5. Which moving object is travelling the fastest?
      
      
      Check your work.
      

      B
   6. Which moving object is travelling the slowest?
      
      
      Check your work.
      

      C
   
   
   2. Use the graph provided to answer the following questions.
      The motion of several objects is depicted on the velocity-time graph. Each question may have none, one, or more than one answer. Each letter can be used more than once.
      
      
      
      

      

      C7.17 Velocity-Time graph of several objects

      
      
      
      
      1. Which object(s) is/are at rest?
         
         
         Check your work.
         

         A and E
      2. Which object(s) is/are accelerating?
         
         
         Check your work.
         

         B, C, and D
      3. Which object(s) is/are not moving?
         
         
         Check your work.
         

         A and E
         
      4. Which object(s) change(s) its direction?
         
         
         Check your work.
         

         none
      5. Which accelerating object has the smallest acceleration?
         
         
         Check your work.
         

         B
      6. Which accelerating object has the greatest acceleration?
         
         
         Check your work.
         

         D
         

  Digging Deeper

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Motion capture is the process of recording the movement of objects or people. It is used in filmmaking and video game development, along with having medical and sports applications.

©Wikimedia Commons
C7.18 real-life motion data (left) is acquired on a motion capture platform (centre) and used to determine the posture of the phantom (right)

©Wikimedia Commons
Caption: C7.19 motion capture facial

Movements of one or more actors are recorded several times per second, which can then be converted into an animation frame-by-frame.

Components of the movements of the actors are measured such as distance, displacement, time, speed, velocity, and acceleration. All these measurements are used to convert the movements to a moving image.

Go to the following link https://en.wikipedia.org/wiki/Motion_capture#Methods_and_systems for more information on this topic.   Learn More

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