Chapter 2, Problem 65A

To determine

The sketch of the position time graph corresponding to the particle model diagram,and an equation that describes the motion of chicken.

Explanation of Solution

Given:

The particle model diagram for the motion of chicken is shown.

Formula used:

The expression for the average velocity $\left(\overline{v}\right)$ of the chicken is as follows:

  $\overline{v}=\frac{\Delta x}{\Delta t}$

Here, $\Delta x$ represents the change in position of chicken (measured along vertical axis) and $\Delta t$ represents the time interval (measured along horizontal axis).

The slope of the position versus time graph of the chicken represents the average velocity of the chicken.

Calculation:

From the particle model diagram for the motion of chicken:

The total time taken by the chicken to move from one side of the road to the other side is $1.9\text{s}$ .

The ratio change in position of the chicken to the time interval is a constant.

Hence, the chicken moves with uniform velocity $\left(\overline{v}\right)$ .

Position time graph:

Consider the chicken is initially at one side of the road represented by the origin of the position time graph.

The chicken starts moving across the road with constant velocity $\left(\overline{v}\right)$ and covers $\Delta x$ distance in every time interval $\Delta t$ .

The chicken reaches the other side of the road after walking for $1.9\text{s}$ .

Hence, the position time graph for the motion of chicken is a straight line passing through the origin.

Sketch the position time graph for the motion of chicken is shown as follows:

  

From the graph,

Show the equation of motion of chicken as follows:

  $\begin{array}{l}\overline{v}=\frac{\Delta x}{\Delta t}\\ \Delta x=\overline{v}\Delta t\end{array}$

Conclusion:

Thus, the position time graph for the motion of chicken is shown and the equation describing the motion of chicken is $\Delta x=\overline{v}\Delta t$ .