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
Answered by Expert
Answer:
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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