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.

Plot the rough displacement curve.

• 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.