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CBSE Class 11-science Answered

The relation between distance 'x' and time 't' is t = A(x^2) + Bx , where A and B are constants . The retardation is ?

Asked by arunavamitra50 | 21 Jun, 2018, 06:57: AM

Expert Answer

Given realation for time t and x is,

begin mathsize 12px style t space equals space A space x squared space plus space B space x space.............. left parenthesis 1 right parenthesis end style

let us differentiate eqn.(1) with respect to time , we get :-

begin mathsize 12px style 1 space equals space 2 space A space x space plus space B space fraction numerator d x over denominator d t end fraction end style

.......................(2)

let us differentiate again eqn.(2), we get :-

begin mathsize 12px style 0 space equals space 2 space A space fraction numerator d x over denominator d t end fraction plus B fraction numerator d squared x over denominator d t squared end fraction end style

.................(3)

By substituting for (dx/dt) from 2 and after rearranging, we get :-

begin mathsize 12px style fraction numerator d squared x over denominator d t squared end fraction space equals space fraction numerator 2 space A over denominator B squared end fraction open parentheses 2 space A space x space minus space 1 close parentheses end style

..............................(4)

Answered by Thiyagarajan K | 21 Jun, 2018, 11:06: AM

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