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A particle initially at rest ,starts moving acceleration f ,after t seconds acceleration becomes 2f ,then after 2t seconds ,the acceleration becomes 3f,and increases similarly.Find the velocity of the particle after nt seconds.Also prove that distance travelled in this time is {n(n 1)(2n 1)}× ft²/12.?
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?A particle initially at rest ,starts moving acceleration f ,after t s...

Velocity after nt seconds:
• Let the initial velocity be u and acceleration be a.
• After t seconds, velocity v1 = u + at.
• After 2t seconds, velocity v2 = u + 2at.
• After 3t seconds, velocity v3 = u + 3at.
• This pattern continues, so after nt seconds, velocity vn = u + nat.
• Substitute the values of a and t in terms of f and n to get vn = u + nft.

Distance traveled:
• The distance traveled is given by the formula: s = ut + 0.5at².
• Substitute the values of u and a in terms of f and n to get s = 0.5fn²t².
• Sum of distances traveled over each interval of time is the total distance.
• This is a sum of squares series: ∑n² = n(n+1)(2n+1)/6.
• Multiply by f and t² to get the final result: {n(n-1)(2n-1)}ft²/12.
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?A particle initially at rest ,starts moving acceleration f ,after t seconds acceleration becomes 2f ,then after 2t seconds ,the acceleration becomes 3f,and increases similarly.Find the velocity of the particle after nt seconds.Also prove that distance travelled in this time is {n(n 1)(2n 1)}× ft²/12.?
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?A particle initially at rest ,starts moving acceleration f ,after t seconds acceleration becomes 2f ,then after 2t seconds ,the acceleration becomes 3f,and increases similarly.Find the velocity of the particle after nt seconds.Also prove that distance travelled in this time is {n(n 1)(2n 1)}× ft²/12.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about ?A particle initially at rest ,starts moving acceleration f ,after t seconds acceleration becomes 2f ,then after 2t seconds ,the acceleration becomes 3f,and increases similarly.Find the velocity of the particle after nt seconds.Also prove that distance travelled in this time is {n(n 1)(2n 1)}× ft²/12.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?A particle initially at rest ,starts moving acceleration f ,after t seconds acceleration becomes 2f ,then after 2t seconds ,the acceleration becomes 3f,and increases similarly.Find the velocity of the particle after nt seconds.Also prove that distance travelled in this time is {n(n 1)(2n 1)}× ft²/12.?.
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