Chapter 2, Problem 38P

(a)

To determine

To draw: The graph of speed as a function of time.

Answer to Problem 38P

The graph of speed is shown in Figure 1.

Explanation of Solution

Given:

The object’s initially at rest and falls under the influence of gravity.

Formula used:

Newton’s first equation of motion,

  $v=u+at$

Calculation:

Using the above formula, the speed of the object will be

  $\begin{array}{l}v=0+9.8\times t\\ v\propto t\end{array}$

The graph for the speed with respect to time is shown below.

  

Figure 1

In the above graph, x -axis represents time in seconds and y -axis represents speed in meter seconds.

Conclusion:

Thus, the speed as a function of time is shown graphically in Figure 1.

(b)

To determine

To draw: A graph of distance fallen as a function of time.

Answer to Problem 38P

The graph is shown in Figure 2

Explanation of Solution

Given:

The object’s initially at rest and falls under the influence of gravity.

Formula used:

Using Newton’s second equation of motion,

  $s=ut+\frac{1}{2}a{t}^2$

Calculation:

Using the above formula, the distance traveled by the object will be

  $\begin{array}{l}s=0+\frac{1}{2}\times 9.8\times t^2\\ s=4.9\times t^2\\ s\propto t^2\end{array}$

The distance time graph is shown in figure 2.

  

Figure 2

In the graph shown above, y -axis represents distance fallen in meters while x -axis represents the time in seconds.

Conclusion:

Thus, the distance fallen as a function of time will be a parabola as shown in Figure 2.