Chapter 1, Problem 4STP

To determine

To Choose: The correct option.

Answer to Problem 4STP

Option A: $\text{0}\text{.25}{\text{m/s}}^2$ .

Explanation of Solution

Given:

The graph of speed $\left(\text{m/s}\right)$ versus time $\left(\text{s}\right)$ .

Formula used:

The expression for slope $\left(m\right)$ of the speed $\left(\text{m/s}\right)$ versus time $\left(\text{s}\right)$ graph is as follows:

  $m=\frac{\Delta y}{\Delta x}$

Here, $\Delta y$ represents the change in speed (measured along vertical axis) and $\Delta x$ represents the change in time (measured along horizontal axis).

The slope of the speed versus time graph of any object represents the acceleration of the object.

Calculation:

Show the speed $\left(\text{m/s}\right)$ versus time $\left(\text{s}\right)$ graph as follows:

  

Find the slope of the graph as follows:

  $\begin{array}{l}m=\frac{\Delta y}{\Delta x}\\ m=\left(\frac{1\text{m/s}-0.5\text{m/s}}{4\text{s}-2\text{s}}\right)\\ m=\left(\frac{0.5\text{m/s}}{2\text{s}}\right)\\ m=\left(\frac{0.5\text{m/s}}{2\text{s}}\right)\\ m=0.25{\text{m/s}}^2\end{array}$

The slope of the speed versus time graph is $m=0.25{\text{m/s}}^2$ .

Conclusion:

Hence, the correct option is $A$ .