The displacement of a particle a time t is given by where a, b and c are positive constants. Then the particle: is

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Q: 98 (NDA-I/2013)
The displacement of a particle a time t is given by where a, b and c are positive constants. Then the particle: is

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,5,2,5,1,1,0

keywords: 

{'displacement': [0, 1, 0, 3], 'particle': [0, 2, 8, 30], 'positive constants': [0, 0, 0, 1]}

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.