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  • Calculating Average Velocity with Variable Acceleration: A Step-by-Step Guide
    Here's how to solve this problem step-by-step:

    1. Calculate the velocity after 6 seconds:

    * Initial velocity (v₀) = 0 m/s (at rest)

    * Acceleration (a) = 1.7 m/s²

    * Time (t) = 6 s

    * Final velocity (v) = v₀ + at = 0 + (1.7 m/s²)(6 s) = 10.2 m/s

    2. Calculate the total distance traveled:

    * Distance traveled during acceleration (d₁) = (1/2)at² = (1/2)(1.7 m/s²)(6 s)² = 30.6 m

    * Distance traveled at constant velocity (d₂) = v * t = (10.2 m/s)(9 s) = 91.8 m

    * Total distance (d) = d₁ + d₂ = 30.6 m + 91.8 m = 122.4 m

    3. Calculate the average velocity:

    * Average velocity (v_avg) = Total distance / Total time = 122.4 m / 15 s = 8.16 m/s

    Therefore, the object's average velocity over the 15-second interval is 8.16 m/s.

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