TS EAMCET · Physics · Work Power Energy
A body of mass 0.5 kg is supplied with a power ' P ' (in watt) which varies with time ' t ' (in second) as \(\mathrm{P}=3 \mathrm{t}^2+3\). If the velocity of the body at time \(\mathrm{t}=0\) is zero, then the velocity of the body at time \(t=3 \mathrm{~s}\) is
- A \(12 \mathrm{~ms}^{-1}\)
- B \(24 \mathrm{~ms}^{-1}\)
- C \(18 \mathrm{~ms}^{-1}\)
- D \(36 \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(A) \(12 \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
\(W = \int P dt = \int_0^t (3t^2+3) dt\) \(W = [t^3+3t]_0^t = t^3+3t\) \(W(t=3) = (3)^3+3(3) = 27+9 = 36 \mathrm{~J}\) \(W = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2\) \(36 = \frac{1}{2}(0.5)v^2 - 0\) \(36 = 0.25v^2\) \(v^2 = \frac{36}{0.25} = 144\)…
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