Question

The function s=-t³+6 t²-12 t, 0 ≤ t ≤ 3, gives the position of a body moving on a coordinate line, with s in meters and t in seconds. . Find the body's displacement and average velocity for the given time interval

Answer 1

The body's displacement is -9 meters and the average velocity is -3 m/s.

Step-by-step explanation:

To find the body's displacement, we need to calculate the change in position between the initial and final time. Since the initial position is not given, we can find it by plugging in 0 for t in the position function. s(0) = 0³ - 6(0)² + 12(0) = 0. So the initial position is 0. To find the final position, we plug in 3 for t. s(3) = -3³ + 6(3)² - 12(3) = -27 + 54 - 36 = -9. So the final position is -9.

The displacement is then given by the formula Δs = s(final) - s(initial). Therefore, Δs = -9 - 0 = -9 meters.

To find the average velocity, we use the formula v(avg) = Δs / Δt, where Δt is the time interval. In this case, the time interval is 3 - 0 = 3 seconds. Therefore, v(avg) = -9 / 3 = -3 m/s.