The position of an object moving along a line is given by...

The position of an object moving along a line is given by the function s(t) = - 12t ^ 2 + 96t Find the average velocity of the object over the following intervals (a) [1, 4] (c) [1, 2] (b) [1, 3] ( d) [1, 1 + h] where h > 0 is any real number ( a) The average velocity of the object over the interval [1, 4] is (b) The average velocity of the object over the interval [1, 3] is ) The average velocity of the object over the interval [1, 2] is ( d) The average velocity of the object over the interval [1,1+h]| is

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Transcript

00:01 In this question, we are asked to find the average velocity of the object with a given position function over the given intervals.

00:10 So, to find the average velocity over the interval from 1 to 5, we need to calculate s of 5 minus 1 divided by 5 minus 1.

00:25 Let's calculate s of 1 because we will need it in all parts of the equation.

00:31 S of 1 equals to negative 20.

00:35 Plus 80 and that's going to be 60 so s of 1 equals to 60 and so now for this particular part we need to also calculate s of 5 so 5 equals to negative 20 times 5 squared plus 80 times 5 squared is 25 25 25 times 25 times 20 is 500 so it's negative 500 plus 400 and equals to negative 100.

01:19 That's s of 5.

01:21 So the average velocity is negative 100 minus 60 divided by 4.

01:30 And negative 160 over 4 equals to negative 40.

01:35 So that's the average velocity in the first case over the interval 15.

01:44 Now let's move on to the next interval.

01:49 In that case, we need to calculate s of 4 minus s of 1 over 4 minus 1.

01:59 Well, let's calculate s of 4.

02:03 S of 4 equals to negative.

02:08 So let me copy this formula.

02:12 And keep in mind that s of 1 equals to 60.

02:22 So this is s of t and therefore s of 4 equals to negative 20 times 16.

02:29 Plus 80 times 4.