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The displacement of a particle at a given time is determined by the given equation . To determine the direction of acceleration, we need to analyze the expression carefully.
In the given equation, we have . This means that the coefficient of the term is positive. Since acceleration is given by the second derivative of displacement with respect to time, a positive coefficient implies that the acceleration is also positive.
The positive acceleration indicates that the particle is being accelerated in the positive % -direction. This means that the velocity of the particle is increasing in the positive % -direction over time.
Therefore, option 1, which states that the particle is accelerated along the % -direction, is correct.
It is important to note that options 2, 3, and 4 mention deceleration. However, since the coefficient of the term is positive, deceleration is not occurring. The particle is accelerating along the % -direction.
Hence, the provided answer is correct and no alert is required.