To calculate the acceleration of the hoop, you can use the formula for acceleration:
\[ a = \frac{\Delta v}{\Delta t} \]
where \( \Delta v \) is the change in velocity and \( \Delta t \) is the time interval.
Here, the initial velocity \( v_i = 2.0 , \text{m/s} \) and the final velocity \( v_f = 12.0 , \text{m/s} \), so:
\[ \Delta v = v_f - v_i = 12.0 , \text{m/s} - 2.0 , \text{m/s} = 10.0 , \text{m/s} \]
The time interval \( \Delta t = 6.0 , \text{s} \). Now, plug this into the acceleration formula:
\[ a = \frac{10.0 , \text{m/s}}{6.0 , \text{s}} \approx 1.67 , \text{m/s}^2 \]
Thus, the acceleration of the hoop is approximately \( 1.67 , \text{m/s}^2 \).