Question

A particle is moving along a straight line according to some position function $s\left(t\right)$. The distance (in feet) of the particle, s, from its starting point after t seconds is given in the table. Find the average rate of change of distance from $t=3$to $t=6$seconds

Short answer

The average speed is$35\frac{1}{3}\frac{\text{feet}}{\text{second}}$.

Step-by-step solution

Step 1. Given information

We are given a table with different values of $t,s$

We need to find the average speed using the given data,

Step 2. Calculation of average speed

The average speed can be fount by $\frac{\mathbf{\Delta }\mathbf{s}}{\mathbf{\Delta }\mathbf{t}}$

When$$\begin{gathered} t=6,s=137 \\ t=3,s=31 \\ \frac{\Delta s}{\Delta t}=\frac{s\left(6\right)-s\left(3\right)}{6-3} \\ =\frac{137-31}{3} \\ =\frac{106}{3} \\ 35\frac{1}{3}\frac{\text{feet}}{\text{second}} \end{gathered}$$