Question

8.) plot an acceleration vs. time graph for the acceleration of an object dropped from a very large height for the first 5 seconds of its fall. make sure that you label the axes appropriately.

Explanation:

When an object is dropped from a large height (assuming we ignore air resistance, a standard introductory physics assumption), its acceleration remains constant due to Earth's gravity for the first 5 seconds of fall. The constant acceleration near Earth's surface is approximately $9.8\ \text{m/s}^2$. The acceleration vs. time graph will be a horizontal line, as acceleration does not change with time in this scenario. Axes are labeled with the independent variable (time, in seconds) on the x-axis and dependent variable (acceleration, in $\text{m/s}^2$) on the y-axis.

Answer:

Acceleration vs. Time Graph Details:

1. X-axis Label: Time ($t$), units: seconds (s), range: 0 to 5 s
2. Y-axis Label: Acceleration ($a$), units: $\text{m/s}^2$, range: 0 to $10\ \text{m/s}^2$
3. Graph Line: A horizontal straight line at $a = 9.8\ \text{m/s}^2$, spanning from $t=0\ \text{s}$ to $t=5\ \text{s}$ (this line does not slope, as acceleration is constant with no air resistance).