Chapter 2, Problem 5P

To determine

The average velocity of the rolling ball.

Answer to Problem 5P

Average velocity is $-2.45\text{ cm/s}$ .

Explanation of Solution

Given:

Rolling ball moves from $x_1=3.4$ cm to $x_2=-4.2$ cm during the time from $t_1=3.0$ s to $t_2=6.1$ s.

Formula used:

Average velocity $\overline{v}=\frac{x_2-x_1}{t_2-t_1}=\frac{\Delta x}{\Delta t}$

Calculation:

For the motion in one direction, average speed and average velocity have the same magnitude.

Substituting the given values,

  $\begin{array}{c}\overline{v}=\frac{-4.2-3.4}{6.1-3.0}\\ =\frac{-7.6}{3.1}\text{cm/s}\\ \text{=}-2.45\text{cm/s}\end{array}$

Average velocity is negative. This means that the rolling ball is moving to the left along the x-axis.

Conclusion:

Therefore, the average velocity is $-2.45\text{cm/s}$