Chapter 2, Problem 42R

To determine

Todraw:the distance-time graph that shows the motion of both runners.

To calculate: the average speed of each member.

To find:the runner which stops briefly.

To evaluate: the time interval in which both of them have same speed.

Answer to Problem 42R

The average speed of each member are $\boxed{v=2\text{m/s}}$ and $\boxed{v=1\text{m/s}}$ respectively. A stopped briefly. The speed of the sally and A will never be equal at any time interval.

Explanation of Solution

Given:

The given table is shown below:

Distance – time for runners
Time (s)	1	2	3	4
Sally’s distance (m)	2	4	6	8
A’s distance (m)	1	2	2	4

Formula used:

The total distance travelled over the total time is average speed and it is expressed as,

  $v=\frac{d_f-d_i}{\Delta t}$.............(1)

Here, $d_f$ and $d_i$ are final and initial distance respectively.

Calculation:

The tabular form for the distance-time graph is shown below:

Time	Sally distance	A distance
0	0	0
1	2	1
2	4	2
3	6	2
4	8	4

The graphical representation of the motion is

  

The average speed of sally is calculated by substitute 8 m for $d_f$ , 0 m for $d_i$ and 4 s for $t$ in equation (1)

  $\begin{array}{l}v=\frac{\left(8-0\right)\text{m}}{4\text{s}}\\ \boxed{v=2\text{m/s}}\end{array}$

The average speed of A is calculated by substitute 4 m for $d_f$ , 0 m for $d_i$ and 4 s for $t$ in equation (1)

  $\begin{array}{l}v=\frac{\left(4-0\right)\text{m}}{4\text{s}}\\ \boxed{v=1\text{m/s}}\end{array}$

From the above graph, it is clear that A stopped briefly from $t=2\text{s}$ to $t=3\text{s}$ .

The speed of the sally and A is never same. The graph or slope doesn’t have same value at any point of time interval.

Conclusion:

Hence, the average speed of each member are $\boxed{v=2\text{m/s}}$ and $\boxed{v=1\text{m/s}}$ respectively.A stopped briefly. The speed of the sally and A will never be equal at any time interval.