16. 0 / 4 points the figure shows the graphs of four functions. one is the position function of a car, one…
16. 0 / 4 points the figure shows the graphs of four functions. one is the position function of a car, one is the velocity of the car, one is its acceleration, and one is its jerk. identify each curve, and explain your choices. position a × velocity d × acceleration a × jerk c ×
Answer
Explanation:
Step1: Recall derivative relationships
Velocity is the derivative of position, acceleration is the derivative of velocity, and jerk is the derivative of acceleration.
Step2: Analyze the smooth - ness and turning points
The position function is usually the most "smooth" in terms of overall shape. The curve (d) has a relatively smooth and continuous increase, which is characteristic of a position function as position changes continuously over time.
Step3: Analyze velocity
The velocity function (c) has positive and negative values. When the velocity is positive, the position is increasing, and when it's negative, the position is decreasing. The zero - crossings of velocity correspond to the turning points of the position function.
Step4: Analyze acceleration
The acceleration function (b) has zero - crossings which correspond to the turning points of the velocity function. When acceleration is positive, velocity is increasing, and when it's negative, velocity is decreasing.
Step5: Analyze jerk
The jerk function (a) has a more "wiggly" behavior as it is the derivative of acceleration. It changes sign multiple times, which is consistent with the changes in the concavity of the acceleration function.
Answer:
Position: (d) Velocity: (c) Acceleration: (b) Jerk: (a)