1. **State the problem:** We want to approximate the distance traveled by a particle over the time interval $0 \leq t \leq 8$ seconds using the midpoint Riemann sum with four subintervals. 2. **Recall the formula:** The midpoint Riemann sum for approximating the integral $\int_a^b f(t) dt$ with $n$ subintervals is $$\sum_{i=1}^n f\left(\frac{t_{i-1} + t_i}{2}\right) \Delta t$$ where $\Delta t = \frac{b-a}{n}$ and the midpoint of each subinterval is $\frac{t_{i-1} + t_i}{2}$. 3. **Apply to this problem:** Here, $a=0$, $b=8$, and $n=4$, so $$\Delta t = \frac{8-0}{4} = 2$$ The subintervals are $[0,2]$, $[2,4]$, $[4,6]$, and $[6,8]$. 4. **Find midpoints:** - Midpoint of $[0,2]$ is $1$ - Midpoint of $[2,4]$ is $3$ - Midpoint of $[4,6]$ is $5$ - Midpoint of $[6,8]$ is $7$ 5. **Evaluate velocity at midpoints:** From the table, - $v(1) = 7$ - $v(3) = 6$ - $v(5) = 7$ - $v(7) = 3$ 6. **Calculate the midpoint Riemann sum:** $$\text{Distance} \approx \Delta t \times \left[v(1) + v(3) + v(5) + v(7)\right] = 2 \times (7 + 6 + 7 + 3)$$ $$= 2 \times 23 = 46$$ 7. **Check for simplification or errors:** The user states the answer is 48, but calculation shows 46. The midpoint Riemann sum calculation is correct based on the given data. **Final answer:** $$\boxed{46}$$ meters is the approximate distance traveled using the midpoint Riemann sum with four subintervals.