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 + 120t. Find the average velocity of the object over the following intervals. (a) [1, 6] (b) [1, 5] (c) [1, 4] (d) [1, 1 + h] where h > 0 is any real number.

Transcript

00:01 In this problem we are given the function s of t is equal to negative 12 t square plus 120 t and this function denotes the position of a particle moving along a line.

00:14 We are asked to find the average velocity in different time intervals.

00:18 The first time interval is 1 .6.

00:21 Now let v average denote the average velocity.

00:24 Then it is the average rate of change of this s of t because velocity is the rate of change.

00:31 Of the displacement function here it is the position function now by definition for a function f of x the average rate of change of the function in an interval closed interval a b is denoted as f average and it is defined as f of b minus f of a divided by b minus a here in this interval the average velocity is the average rate of change of the position function by definition it is s of 6 minus s of 1 by so 6 minus 1.

01:02 Now s of 6 is obtained by substituting in s of t, the value t is equal to 6.

01:07 So that is negative 12 times 6 square plus 120 times 6 which is negative 432 plus 720 plus 720 which is 288.

01:24 So that s of 6 is 288.

01:26 Similarly s of 1 is negative 12 plus 120.

01:30 That is when obtained it is obtained when substituting t is equal to 1 in s of t and that is 1 .8 so that the average velocity during this time interval is 288 minus 108 divided by 5 which is 180 by 5 upon simplification this is 36 so that the average velocity during this time interval is 36.

01:53 The second time interval is interval 15 and in this interval the average velocity is is calculated as the average rate of change of the position function that is s of 5 minus s of 1 by 5 minus 1...

Question

The position of an object moving along a line is given by the function s(t) = -12t^2 + 120t. Find the average velocity of the object over the following intervals. (a) [1, 6] (b) [1, 5] (c) [1, 4] (d) [1, 1 + h] where h > 0 is any real number.

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