Question

1. 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 ×

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: \(a\)