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A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t2 + t3, where x is in metres and t is in seconds. The work done during the first 4 seconds is [1998]
  • a)
    576 mJ
  • b)
    450 mJ
  • c)
    490 mJ
  • d)
    530 mJ
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A force acts on a 30 gm particle in such a way that the position of th...
x = 3t –4t2 + t3
Acceleration 
Acceleration after 4sec = –8 + 6 × 4 = 16 ms–2
Displacement in 4sec = 3 ×4 – 4 × 42 + 43 = 12 m
∴  Work = Force × displacement = Mass × acc. × disp. = 3 × 10–3 × 16 × 12 = 576 mJ
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Most Upvoted Answer
A force acts on a 30 gm particle in such a way that the position of th...
To find the force acting on the particle, we need to differentiate the position function x with respect to time t.

Given: x = 3t

Differentiating both sides with respect to time, we get:

dx/dt = d(3t)/dt

The derivative of 3t with respect to t is simply 3.

Therefore, the velocity of the particle is dx/dt = 3.

Since force is equal to the rate of change of momentum, which is mass multiplied by velocity, we can calculate the force acting on the particle.

Given: mass = 30 grams = 0.03 kg, velocity = 3 m/s

Force = mass * velocity = 0.03 kg * 3 m/s = 0.09 N

Therefore, the force acting on the 30 gm particle is 0.09 N.
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A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t2 + t3, where x is in metres and t is in seconds. The work done during the first 4 seconds is [1998]a)576 mJb)450 mJc)490 mJd)530 mJCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t2 + t3, where x is in metres and t is in seconds. The work done during the first 4 seconds is [1998]a)576 mJb)450 mJc)490 mJd)530 mJCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t2 + t3, where x is in metres and t is in seconds. The work done during the first 4 seconds is [1998]a)576 mJb)450 mJc)490 mJd)530 mJCorrect answer is option 'A'. Can you explain this answer?.
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