Questions: The function s(t) represents the position of an object at time t moving along a line. Suppose s(1)=115 and s(4)=193. Find the average velocity of the object over the interval of time [1,4]. The average velocity over the interval [1,4] is vav= . (Simplify your answer.)

The function s(t) represents the position of an object at time t moving along a line. Suppose s(1)=115 and s(4)=193. Find the average velocity of the object over the interval of time [1,4].

The average velocity over the interval [1,4] is vav= . (Simplify your answer.)

Transcript text: The function $s(t)$ represents the position of an object at time $t$ moving along a line. Suppose $s(1)=115$ and $s(4)=193$. Find the average velocity of the object over the interval of time [1,4]. The average velocity over the interval $[1,4]$ is $\mathrm{v}_{\mathrm{av}}=$ $\square$ . (Simplify your answer.)

Solution

Solution Steps

Step 1: Identify the Formula for Average Velocity

The average velocity $ v_{\text{av}} $ over a time interval $[t_1, t_2]$ is given by the formula: \[ v_{\text{av}} = \frac{s(t_2) - s(t_1)}{t_2 - t_1} \]

Step 2: Substitute the Given Values

We are given $ s(1) = 115 $ and $ s(4) = 193 $. Substitute these values into the formula: \[ v_{\text{av}} = \frac{193 - 115}{4 - 1} \]

Step 3: Calculate the Average Velocity

Perform the subtraction and division: \[ v_{\text{av}} = \frac{78}{3} = 26 \]