Consider the velocity function $$ v(t)=2 \sin t $$ for $$ 0 \leq t \leq \pi $$. Complete the sentence: The same distance could have been traveled over the given time period at a constant velocity of The same distance could have been traveled over the given time period at a constant velocity of $$ \square $$. (Type an exact answer in terms of $$ \pi $$.)

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To find the constant velocity that results in the same distance traveled over the time interval $$ 0 \leq t \leq \pi $$, follow these steps:

1. **Calculate the Total Distance Traveled:**
   
   The velocity function is $$ v(t) = 2 \sin t $$. Since $$ \sin t $$ is non-negative over $$ [0, \pi] $$, the distance traveled is the integral of the velocity:
   $$
   \text{Distance} = \int_{0}^{\pi} 2 \sin t \, dt = 2 \left[ -\cos t \right]_{0}^{\pi} = 2 \left( -\cos \pi + \cos 0 \right) = 2 (1 + 1) = 4
   $$

2. **Determine the Time Interval:**
   
   The total time is $$ \pi - 0 = \pi $$.

3. **Find the Equivalent Constant Velocity:**
   
   To find the constant velocity $$ v_{\text{constant}} $$ that covers the same distance in the same time:
   $$
   v_{\text{constant}} = \frac{\text{Distance}}{\text{Time}} = \frac{4}{\pi}
   $$

**Final Answer:**
$$\displaystyle \frac{4}{\pi}$$
The same distance could have been traveled over the given time period at a constant velocity of $$ \frac{4}{\pi} $$.

Consider the velocity function for . Complete the sentence: The same distance could have been traveled over the given
time period at a constant velocity of
The same distance could have been traveled over the given time period at a constant velocity of . (Type an exact answer in terms of .)

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Consider the velocity function for . Complete the sentence: The same distance could have been traveled over the given time period at a constant velocity of The same distance could have been traveled over the given time period at a constant velocity of . (Type an exact answer in terms of .)