Suppose the position of an object moving horizontally along a line after t seconds is given by the following functions s = f(t), where s is measured in feet, with s > 0 corresponding to positions right of the origin.
Determine the acceleration of the object when its velocity is zero.
f(t) = 2t² - 9t + 12; 0 ≤ t ≤ 3

Verified step by step guidance

1. Step 1: Find the velocity function by differentiating the position function s = f(t) with respect to time t. The velocity function v(t) is the first derivative of f(t), so v(t) = f'(t).
2. Step 2: Differentiate f(t) = 2t^2 - 9t + 12 to find v(t). Use the power rule for differentiation: if f(t) = at^n, then f'(t) = nat^(n-1).
3. Step 3: Set the velocity function v(t) equal to zero to find the time(s) when the velocity is zero. Solve the equation v(t) = 0 for t.
4. Step 4: Find the acceleration function by differentiating the velocity function v(t) with respect to time t. The acceleration function a(t) is the second derivative of f(t), so a(t) = v'(t) = f''(t).
5. Step 5: Evaluate the acceleration function a(t) at the time(s) found in Step 3 to determine the acceleration of the object when its velocity is zero.