A particle travels along the x-axis such that its position at time t is given by the function x(t) = 2t2 + t. What is the average speed of this particle over the interval 2 ≤ t ≤ 10?

The position function is increasing on 2 ≤ t ≤ 10, so the particle does not reverse direction and its distance traveled is x(10) − x(2). Substituting gives x(10) = 2(10²) + 10 = 210 and x(2) = 2(2²) + 2 = 10. The elapsed time is 10 − 2 = 8, so average speed is (210 − 10) ÷ 8 = 25. The correct choice is 25.

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