Question

a student is investigating the motion of a coffee filter as it falls to the ground through the air. a graph of the velocity v of the coffee filter as a function of time t is shown in the figure. which of the following describes the changes in the magnitude of the acceleration and magnitude of resistive force of the coffee filter as it falls?
acceleration\tresistive force
a\tdecreasing\tdecreasing
b\tdecreasing\tincreasing
c\tincreasing\tdecreasing
d\tincreasing\tincreasing

Explanation:

Step1: Recall acceleration - velocity relationship

Acceleration is the slope of the velocity - time graph. The slope of the given $v - t$ graph is decreasing as time progresses. So the magnitude of the acceleration is decreasing.

Step2: Analyze force equilibrium and resistive force

The forces acting on the coffee - filter are gravitational force $F_g = mg$ (downward) and resistive force $F_r$ (upward). According to Newton's second law $F_{net}=ma = mg - F_r$. As $a$ decreases (from Step 1) and $mg$ is constant, the resistive force $F_r=mg - ma$ must be increasing.

Answer:

B. Decreasing, Increasing