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# Initial acceleration of a particle moving in a straight line is A and initial velocity is zero. The acceleration reduces continuously to half in every t seconds. The terminal velocity of the particle is:

Asked by Arushi Juyal 12th November 2017, 3:04 PM
Initially particle starts from rest and moving with acceleration A. Hence final velocity after time t is (A×t).
After time t the acceleration reduces to A/2, hence the final velocity at end of time 2t is given by [ A×t +  (1/2)×A×t ]
Again the acceleration is reduces to half, hence the acceleration after time 2t is A/4.
Final velocity is [ At + (1/2)×A×t + (1/4)×A×t ].
This goes on and the terminal velocity can be written as [ A×t + (1/2)×A×t + (1/4)×A×t + (1/8)×A×t + (1/16)×A×t  ]

The above bracketted term is written as A×t × [ 1 + (1/2) + (1/4) + (1/8) + (1/16) + •   ] = A×t×2

Hence the terminal velocity is 2×A×t
Answered by Expert 13th November 2017, 12:32 PM
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