### Critical Thinking Items

## 3.2 Representing Acceleration with Equations and Graphs

A student is asked to solve a problem:

An object falls from a height for 2.0 s, at which point it is still 60 m above the ground. What will be the velocity of the object when it hits the ground?

Which of the following provides the correct order of kinematic equations that can be used to solve the problem?

- First use ${v}^{2}={v}_{0}{}^{2}+2a(d-{d}_{0})\text{,}$ then use $v={v}_{0}+at.$
- First use $v={v}_{0}+at,$ then use ${v}^{2}={v}_{0}{}^{2}+2a(d-{d}_{0})\text{.}$
- First use $d={d}_{0}+{v}_{0}t+\frac{1}{2}a{t}^{2},$ then use $v={v}_{0}+at.$
- First use $v={v}_{0}+at,$ then use $d-{d}_{0}={v}_{0}t+\frac{1}{2}a{t}^{2}.$

Skydivers are affected by acceleration due to gravity and by air resistance. Eventually, they reach a speed where the force of gravity is almost equal to the force of air resistance. As they approach that point, their acceleration decreases in magnitude to near zero.

Part A. Describe the shape of the graph of the magnitude of the acceleration versus time for a falling skydiver.

Part B. Describe the shape of the graph of the magnitude of the velocity versus time for a falling skydiver.

Part C. Describe the shape of the graph of the magnitude of the displacement versus time for a falling skydiver.

- Part A. Begins with a nonzero y-intercept with a downward slope that levels off at zero; Part B. Begins at zero with an upward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant
- Part A. Begins with a nonzero y-intercept with an upward slope that levels off at zero; Part B. Begins at zero with an upward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant
- Part A. Begins with a nonzero y-intercept with a downward slope that levels off at zero; Part B. Begins at zero with a downward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant
- Part A. Begins with a nonzero y-intercept with an upward slope that levels off at zero; Part B. Begins at zero with a downward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant

Which graph in the previous problem has a positive slope?

- Displacement versus time only
- Acceleration versus time and velocity versus time
- Velocity versus time and displacement versus time
- Acceleration versus time and displacement versus time