WBJEE · Maths · Application of Derivatives
Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and \(f\) ' respectively. If \(A\) takes \(\mathrm{m}\) sec. more than that of \(\mathrm{B}\) and describes \(\mathrm{n}\) units more than that of \(\mathrm{B}\) in acquiring the same velocity, then
- A \(\left(f+f^{\prime}\right) m^{2}=\) ff'n
- B \(\left(f-f f^{\prime}\right) m^{2}=f f^{\prime} n\)
- C \(\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}\)
- D \(\frac{1}{2}\left(\mathrm{f}+\mathrm{f}^{\prime}\right) \mathrm{m}=\mathrm{ff}^{\prime} \mathrm{n}^{2}\)
Answer & Solution
Correct Answer
(C) \(\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{llll}A:\quad u=0 & a_{1}=f & t_{1}=t+m & s_{1}=n+s \\ B: \quad u=0 & a_{2}=f^{\prime} & t_{2}=t & s_{2}=s\end{array}\) \(\mathrm{s}+\mathrm{n}=\frac{1}{2} \mathrm{f} .(\mathrm{t}+\mathrm{m})^{2} \ldots \ldots(\mathrm{i}) \quad\) and…
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