WBJEE · Maths · Application of Derivatives
The displacement \(\mathrm{x}\) of a particle at time \(\mathrm{t}\) is given by \(\mathrm{x}=\mathrm{At}^2+\mathrm{Bt}+\mathrm{C}\) where \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) are constants and \(\mathrm{v}\) is velocity of a particle, then the value of \(4 \mathrm{Ax}-\mathrm{v}^2\) is
- A \(4 \mathrm{AC}+\mathrm{B}^2\)
- B \(4 \mathrm{AC}-\mathrm{B}^2\)
- C \(2 \mathrm{AC}-\mathrm{B}^2\)
- D \(2 \mathrm{AC}+\mathrm{B}^2\)
Answer & Solution
Correct Answer
(B) \(4 \mathrm{AC}-\mathrm{B}^2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hints: } \mathrm{x}=\mathrm{At}^2+\mathrm{Bt}+\mathrm{c} \\ & \mathrm{v}=2 \mathrm{At}+\mathrm{B} \Rightarrow \mathrm{v}^2=4 \mathrm{~A}^2 \mathrm{t}^2+4 \mathrm{AB} \mathrm{t}+\mathrm{B}^2 \\ & 4 \mathrm{Ax}=4 \mathrm{~A}^2 \mathrm{t}^2+4 \mathrm{AB}…
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