Final answer:
The position of a particle moving along the x-axis is a Vector, as it includes both magnitude and direction. The acceleration can be calculated from the derivative of a given velocity function and the position by integrating the velocity function from the initial time.
Step-by-step explanation:
The position of a particle moving along the x-axis can best be described by option B) Vector. This is because the position in this context is defined not only by a magnitude but also by a direction along the x-axis. Let's now calculate the acceleration and position of the particle using the provided velocity function v(t) = A + Bt¯¹, with A = 2 m/s and B = 0.25 m. The acceleration is the time derivative of velocity, so a(t) = -Bt¯¹². At t = 2.0 s and t= 5.0 s, the accelerations are a(2.0) = -0.25/(2²) = -0.0625 m/s² and a(5.0) = -0.25/(5²) = -0.01 m/s², respectively.
To find the position x(t), we integrate the velocity function from the initial time t=1 s to the current time. Since the initial position x(1) = 0, the integral of the velocity function from 1 s to t seconds will give us x(t) - x(1), which is the displacement. Specifically, x(t) - x(1) = ∫ v(t) dt from t=1 to t. Integrating, we find the position at the times of interest.
Lastly, option C) Accelerated and D) Stationary are not applicable to the position directly but can describe the state of motion based on whether the particle's speed is changing (Accelerated) or remains at zero (Stationary).
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