If you are traveling at $35\text{ mph}$ and then slow down to $15\text{ mph}$ over a distance of $0.5\text{ miles}$ as you enter a school zone, what is your average velocity during this interval?

• A. $\frac{50}{2}$ mph
• B. $\frac{35+15}{2}$ mph
• C. $\frac{25}{1}$ mph
• D. $15$ mph

Answer: (B)

Verified step by step guidance

1. Identify the initial velocity \(v_i = 35\) mph and the final velocity \(v_f = 15\) mph, and the distance over which the velocity changes, \(d = 0.5\) miles.
2. Since the velocity changes uniformly over the distance, the average velocity \(v_{avg}\) can be found by taking the arithmetic mean of the initial and final velocities.
3. Write the formula for average velocity when acceleration is constant: \[v_{avg} = \frac{v_i + v_f}{2}\]
4. Substitute the given values into the formula: \[v_{avg} = \frac{35 + 15}{2}\]
5. Simplify the expression to find the average velocity during the interval.