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A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?
- a)Uniform retardation
- b)Uniform speed
- c)Uniform acceleration
- d)Uniform velocity
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A particle moves in a straight-line OA; the distance of the particle f...
The velocity of the particle at time t is given by:
v(t) = dx/dt = abt + 2c^2t
The acceleration of the particle at time t is given by:
a(t) = dv/dt = ab + 4ct
Since the particle moves in a straight line, the acceleration is constant. Therefore, we can find the average acceleration over a time interval [t1, t2] by taking the difference in velocity and dividing by the time interval:
average acceleration = (v(t2) - v(t1))/(t2 - t1)
= [abt2 + 2c^2t2 - (abt1 + 2c^2t1)]/(t2 - t1)
= ab(t2 - t1)/(t2 - t1) + 2c^2(t2 - t1)/(t2 - t1)
= ab + 2c^2
Therefore, the average acceleration of the particle over any time interval is equal to ab + 2c^2.
v(t) = dx/dt = abt + 2c^2t
The acceleration of the particle at time t is given by:
a(t) = dv/dt = ab + 4ct
Since the particle moves in a straight line, the acceleration is constant. Therefore, we can find the average acceleration over a time interval [t1, t2] by taking the difference in velocity and dividing by the time interval:
average acceleration = (v(t2) - v(t1))/(t2 - t1)
= [abt2 + 2c^2t2 - (abt1 + 2c^2t1)]/(t2 - t1)
= ab(t2 - t1)/(t2 - t1) + 2c^2(t2 - t1)/(t2 - t1)
= ab + 2c^2
Therefore, the average acceleration of the particle over any time interval is equal to ab + 2c^2.
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Community Answer
A particle moves in a straight-line OA; the distance of the particle f...
We have, x = a + bt + ct2 ……….(1)
Let, v and f be the velocity and acceleration of a particle at time t seconds.
Then, v = dx/dt = d(a + bt + ct2)/dt = b + ct ……….(2)
And f = dv/dt = d(b + ct)/dt = c ……….(3)
Clearly, when c = 0, then f = 0 that is, acceleration of the particle is zero.
Hence in this case the particle moves with an uniform velocity.
Let, v and f be the velocity and acceleration of a particle at time t seconds.
Then, v = dx/dt = d(a + bt + ct2)/dt = b + ct ……….(2)
And f = dv/dt = d(b + ct)/dt = c ……….(3)
Clearly, when c = 0, then f = 0 that is, acceleration of the particle is zero.
Hence in this case the particle moves with an uniform velocity.
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A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer?
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A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer?.
A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?a)Uniform retardationb)Uniform speedc)Uniform accelerationd)Uniform velocityCorrect answer is option 'D'. Can you explain this answer?.
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