Question

a particle moves along a line so that its position at anytime t is given by the function s(t)=t^3-6t^2+8t+2 where s is measured in meters and t is measured in seconds. Find the average velocity between times t = 1 and t = 2

Answer 1

To find the average velocity of the particle between times t = 1 and t = 2, you can use the following formula:

Average Velocity = (Change in Position) / (Change in Time)

In this case, the change in time is from t = 1 to t = 2, so Δt = 2 - 1 = 1 second.

Now, let's find the change in position:

s(2) - s(1) = [(2)^3 - 6(2)^2 + 8(2) + 2] - [(1)^3 - 6(1)^2 + 8(1) + 2]

s(2) - s(1) = [8 - 24 + 16 + 2] - [1 - 6 + 8 + 2]

s(2) - s(1) = [26] - [5]

s(2) - s(1) = 21 meters

Now, we can calculate the average velocity:

Average Velocity = (Change in Position) / (Change in Time) = 21 meters / 1 second = 21 m/s

So, the average velocity of the particle between times t = 1 and t = 2 is 21 meters per second.