Question

The function​ s(t) represents the position of an object at time t moving along a line. Suppose s(2)=150 and s(5)=237. Find the average velocity of the object over the interval of time [1, 3].

Answer 1

The average velocity of the object over the interval [1, 3] is 43.5 units of distance per unit of time.

Step-by-step explanation:

The average velocity of an object over an interval of time is found by dividing the change in position by the change in time. In this case, we want to find the average velocity of the object over the interval [1, 3].

To do this, we first need to find the change in position during this interval. Given that s(2) = 150 and s(5) = 237, we can calculate the change in position as follows:

s(3) - s(1) = (s(5) - s(3)) + (s(3) - s(1))

Therefore, the average velocity is (s(3) - s(1)) / (3 - 1). By substituting the given values, we find that the average velocity is (237 - 150) / (3 - 1) = 87 / 2 = 43.5 units of distance per unit of time.

Answer 2

29 is answer.

Step-by-step explanation:

Given that the function​ s(t) represents the position of an object at time t moving along a line. Suppose s(2)=150 and s(5)=237.

To find average velocity of the object over the interval of time [1,3]

We know that derivative of s is velocity and antiderivative of velocity is position vector .

Since moving along a line equation of s is

use two point formula

`(s-150)/(237-150) =(t-2)/(5-2) \\s=29t-58+150\\s=29t+92` gives the position at time t.

Average velocity in interval (1,3)

=
`(1)/(3-1) (s(3)-s(1))\\=(1)/(2) [87+58-29-58]\\=29`