Question

1. the function s(t) represents the position of an object at time t moving along a line. suppose s(2) = 136 and s(3) = 156. find the average velocity of the object over the interval of time 2, 3.

Explanation:

Step1: Recall the formula for average velocity

The average velocity \( v_{avg} \) over the interval \([t_1, t_2]\) is given by the change in position divided by the change in time, i.e., \( v_{avg}=\frac{s(t_2)-s(t_1)}{t_2 - t_1} \).
Here, \( t_1 = 2 \), \( t_2 = 3 \), \( s(t_1)=s(2) = 136 \), and \( s(t_2)=s(3)=156 \).

Step2: Substitute the values into the formula

First, calculate the change in position: \( s(3)-s(2)=156 - 136=20 \).
Then, calculate the change in time: \( 3 - 2 = 1 \).
Now, find the average velocity: \( v_{avg}=\frac{156 - 136}{3 - 2}=\frac{20}{1}=20 \).

Answer:

The average velocity of the object over the interval \([2, 3]\) is \( 20 \).