The position of an object moving vertically along a line is given by the function $s\left(t\right)=-4.9t^2+30t+20$. Find the average velocity of the object over the following intervals.
$\left\lbrack0,3\right\rbrack$

Verified step by step guidance

1. To find the average velocity of the object over the interval [0, 3], we need to use the formula for average velocity: \( v_{avg} = \frac{s(t_2) - s(t_1)}{t_2 - t_1} \), where \( t_1 = 0 \) and \( t_2 = 3 \).
2. First, calculate \( s(t_1) = s(0) \) by substituting \( t = 0 \) into the position function \( s(t) = -4.9t^2 + 30t + 20 \). This will give us the initial position of the object.
3. Next, calculate \( s(t_2) = s(3) \) by substituting \( t = 3 \) into the position function. This will give us the position of the object at \( t = 3 \).
4. Subtract \( s(0) \) from \( s(3) \) to find the change in position, \( \Delta s = s(3) - s(0) \).
5. Finally, divide \( \Delta s \) by the change in time, \( \Delta t = 3 - 0 \), to find the average velocity: \( v_{avg} = \frac{\Delta s}{\Delta t} \).