Determine the average acceleration for x(t)=19t^2+7t^3 for a time interval between 3 and 9 seconds

290

Explanation:

Average acceleration is the change in velocity over change in time.

First, find the velocity by taking the derivative of position.

v(t) = dx/dt

v(t) = 38t + 21t²

At t = 3 and t = 9:

v(3) = 303

v(9) = 2043

So the average acceleration is:

a = Δv / Δt

a = (2043 − 303) / (9 − 3)

a = 290

Use appropriate units.