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Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-
- a)46 J
- b)52 J
- c)92 J
- d)104 J
Correct answer is option 'A'. Can you explain this answer?
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Power applied to a particle varies with time as P = (3t2 – 2t + ...
Given Data:
Power function: P = 3t^2 - 2t + 1 (in watts)
Time interval: t = 2s to t = 4s
Calculating Change in Kinetic Energy:
To find the change in kinetic energy, we need to integrate the power function with respect to time over the given time interval.
∆KE = ∫[P(t)] dt (from t = 2 to t = 4)
∆KE = ∫[(3t^2 - 2t + 1)] dt (from 2 to 4)
∆KE = [(t^3 - t^2 + t)] from 2 to 4
∆KE = [(4^3 - 4^2 + 4) - (2^3 - 2^2 + 2)]
∆KE = [(64 - 16 + 4) - (8 - 4 + 2)]
∆KE = [52 - 6]
∆KE = 46 J
Therefore, the change in kinetic energy between t = 2s to t = 4s is 46 Joules, which corresponds to option 'A'.
Power function: P = 3t^2 - 2t + 1 (in watts)
Time interval: t = 2s to t = 4s
Calculating Change in Kinetic Energy:
To find the change in kinetic energy, we need to integrate the power function with respect to time over the given time interval.
∆KE = ∫[P(t)] dt (from t = 2 to t = 4)
∆KE = ∫[(3t^2 - 2t + 1)] dt (from 2 to 4)
∆KE = [(t^3 - t^2 + t)] from 2 to 4
∆KE = [(4^3 - 4^2 + 4) - (2^3 - 2^2 + 2)]
∆KE = [(64 - 16 + 4) - (8 - 4 + 2)]
∆KE = [52 - 6]
∆KE = 46 J
Therefore, the change in kinetic energy between t = 2s to t = 4s is 46 Joules, which corresponds to option 'A'.
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Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-a)46 Jb)52 Jc)92 Jd)104 JCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-a)46 Jb)52 Jc)92 Jd)104 JCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-a)46 Jb)52 Jc)92 Jd)104 JCorrect answer is option 'A'. Can you explain this answer?.
Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-a)46 Jb)52 Jc)92 Jd)104 JCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-a)46 Jb)52 Jc)92 Jd)104 JCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Power applied to a particle varies with time as P = (3t2 – 2t + 1) watts, where t is time in seconds. Then the change in kinetic energy between time t = 2s to t = 4s is-a)46 Jb)52 Jc)92 Jd)104 JCorrect answer is option 'A'. Can you explain this answer?.
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