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AP EAMCET · PHYSICS · Work Power Energy

A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement \((\mathrm{s})\) of the body and time \((\mathrm{t})\) is \(s \propto t^x\), then \(x=\)

  1. A 1
  2. B 2
  3. C \(\frac{2}{3}\)
  4. D \(\frac{3}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

\(P = \frac{d}{dt} \left( \frac{1}{2} mv^2 \right)\) \(Pt = \frac{1}{2}mv^2\) \(v^2 \propto t \Rightarrow v \propto t^{1/2}\) \(\frac{ds}{dt} \propto t^{1/2}\) \(s \propto \int t^{1/2} dt \propto t^{3/2}\) \(s \propto t^x \Rightarrow x = \frac{3}{2}\)