Chapter 2, Problem 1RE

At time t in seconds, a particle’s distance s(t), in cm, from a point is given in the table. What is the average velocity of the particle from t = 3 to t = 10?

To determine

The average velocity of the particle from t = 3 to t = 10.

Answer to Problem 1RE

The average velocity of the particle from t = 3 to t = 10 is $\underset{\_}{10.286\text{ cm/sec}}$.

Explanation of Solution

Formula used:

Average velocity:

“If $s\left(t\right)$ is the position of an object at time t, then the average velocity of the object over the interval $a\le t\le b$ is, $\text{Average velocity}=\frac{\text{Change in position}}{\text{Change in time}}=\frac{s\left(b\right)-s\left(a\right)}{b-a}$”.

Calculation:

Obtain the average velocity of the particle from t = 3 to t = 10.

From the given table, it is observed that, $s\left(3\right)=72,\text{ and }s\left(10\right)=144$.

Here, a = 3 and b = 10.

Substitute a = 3, b = 10, $s\left(3\right)=72,\text{ and }s\left(10\right)=144$ in $\frac{s\left(b\right)-s\left(a\right)}{b-a}$.

$\begin{array}{c}\text{Average velocity}=\frac{s\left(10\right)-s\left(3\right)}{10-3}\\ =\frac{144-72}{10-3}\\ =\frac{72}{7}\\ =10.286\end{array}$

Thus, the average velocity of the particle from t = 3 to t = 10 is $\underset{\_}{10.286\text{ cm/sec}}$.