Question

A particle moves according to the law of motion s=t³-8t², t≥0, where t is measured in seconds and s in feet. (a) Find the average velocity over the interval [1,2].

Answer 1

The average velocity over the interval [1,2] is -5 feet/second.

Step-by-step explanation:

To find the average velocity over the interval [1,2], we need to calculate the displacement of the particle between t = 1 and t = 2. The displacement is the difference in position at these two times. Using the given position function, we can find the position at each time:

s(1) = (1)³ - 8(1)² = -7 feet

s(2) = (2)³ - 8(2)² = -12 feet

The displacement is the difference between these positions: -12 - (-7) = -5 feet.

The average velocity is the displacement divided by the time interval: (-5 feet) / (2 seconds - 1 second) = -5 feet/second.