Question

If a stone is thrown down at 150 ft/s from a height of 1,300 feet, its height after t seconds is given by s = 1,300 − 150t − 16t2. Find its average velocity over the period [1, 3].

Answer 1

To compute the average velocity of a stone over a given time period, one must determine the displacement over that period and divide it by the duration. Here, the average velocity between 1 and 3 seconds is calculated as -214 feet per second, signifying a downward movement.

Step-by-step explanation:

To find the average velocity of the stone over the period from 1 to 3 seconds, we first calculate its height (s) at t = 1s and then at t = 3s using the given function s = 1,300 − 150t − 16t2. Plugging in the values, we get:

• s(1) = 1,300 - 150(1) - 16(1)2 = 1,300 - 150 - 16 = 1,134 feet.
• s(3) = 1,300 - 150(3) - 16(3)2 = 1,300 - 450 - 144 = 706 feet.

The displacement of the stone over this period is s(3) - s(1) = 706 - 1,134 = -428 feet. The time interval is 3 - 1 = 2 seconds. Therefore, the average velocity, vavg, is the displacement divided by the time, which is -428 feet / 2 seconds = -214 feet per second. The negative sign indicates the stone is moving downward.