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MATHEMATICS - CASE STUDY

    Introduction



Remote Control Motorcycle

 

In order to improve her ability to control and operate a remote control car, Judy has decided to analyze the car data, such as velocity, acceleration, weight, fraction, power, and energy. To start the analysis, she examines a basic diagram of the displacement curve of the motorcycle during its operation.

What is known:

  • The operation lasts 30 seconds.
  • From 0 to 10 seconds and 22 to 30 seconds, the acceleration is positive.
  • From 10 to 22 seconds, the acceleration is negative.
  • The velocity is 0 at 7, 14 and 26 seconds.
  • The velocity changes from positive to negative at 7 and 26 seconds.
  • The velocity changes from negative to positive at 14 seconds.
     
    Questions

 

 

Plot the rough displacement curve.

     
    Approach


 
  • Use the Test for Concavity to find the concavity of the function
  • The inflection point is the point where the curve changes from concave upward to concave downward or from concave downward to concave upward.
  • Velocity is the first derivative of displacement with respect to time.
  • Acceleration is the second derivative of displacement with respect to time.