AP EAMCET · PHYSICS · Motion In One Dimension
The relation between time ' \(t\) ' and displacement ' \(x\) ' is \(t=\alpha x^2+\beta x\) where \(\alpha\) and \(\beta\) are constants. If ' \(v\) ' is the velocity, the retardation is
- A \(2 \alpha \nu \beta^2\)
- B \(2 \alpha \beta \nu^3\)
- C \(-2 \beta v^3\)
- D \(2 \alpha v^3\)
Answer & Solution
Correct Answer
(D) \(2 \alpha v^3\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \mathrm{t} & =\alpha \mathrm{x}^2+\beta \mathrm{x} \\ \therefore \frac{\mathrm{dt}}{\mathrm{dt}} & =2 \alpha \mathrm{x} \cdot \frac{\mathrm{dx}}{\mathrm{dt}}+\beta \cdot \frac{\mathrm{dx}}{\mathrm{dt}}=2 \alpha \mathrm{x} \cdot \mathrm{v}+\beta \cdot \mathrm{v}…
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