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CBSE Class 11-science Answered

An object starts from rest moves in constant acceleration A upto its max velocity and then retards at B until it comes to rest Cal the max velocity and the displacement if the total time of journey is T
Asked by sahamamoni597 | 27 Jun, 2023, 01:00: AM
answered-by-expert Expert Answer
Let t1 be the time taken by object to reach maximum velocity vmax with uniform acceleration A . 
 
Then we have,   begin mathsize 14px style v subscript m a x end subscript space equals space A space cross times space t subscript 1 end style
 
begin mathsize 14px style t subscript 1 space equals space v subscript m a x end subscript over A space end style ....................... (1)
 
Let t2 be the time taken by object to come to rest starting from maximum velocity vmax with retardation B . 
 
Then we have, begin mathsize 14px style v subscript m a x end subscript space equals space B space asterisk times space t subscript 2 end style
 
begin mathsize 14px style t subscript 2 space equals space v subscript m a x end subscript over B end style ...........................(2)
 
From eqn.(1) and (2) , we get
 
begin mathsize 14px style t subscript 1 plus t subscript 2 space equals space v subscript m a x space end subscript open parentheses 1 over A plus 1 over B close parentheses end style .................. (3)
It is given that , begin mathsize 14px style t subscript 1 space plus space t subscript 2 space equals space T end style
 
Hence , we get
 
begin mathsize 14px style T space equals space v subscript m a x end subscript open parentheses 1 over A plus fraction numerator 1 over denominator B space end fraction close parentheses space equals space v subscript m a x end subscript space cross times open parentheses fraction numerator A plus B over denominator A space B end fraction close parentheses end style
 
Hence maximum speed is
 
begin mathsize 14px style v subscript m a x end subscript space equals space T space cross times open parentheses fraction numerator A cross times space B over denominator A plus B end fraction close parentheses end style
 
Answered by Thiyagarajan K | 27 Jun, 2023, 02:49: AM

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