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A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proprtional to: 


1. t1/2
2. t3/4
3. t3/2
4. t2

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Best answer
Correct Answer - Option 3 : t3/2

CONCEPT:

Power

  • It is defined as the rate of doing work.

\(⇒ P=\frac{W}{t}=Fv\)

Where W = work, t = time, F = force and v = average velocity

CALCULATION:

Given P = constant and U(initial velocity) = 0 m/s

  • The power is given as,

⇒ P = Fv     -----(1)

By Newton's second law of motion,

⇒  F = ma    -----(2)​

Where F = force, m = mass and a = acceleration

  • The average velocity is given as,

\(⇒ v=\frac{S}{t}\)     -----(3)

Where S = total displacement

By the second equation of motion,

\(⇒ s=ut+\frac{1}{2}at^{2}\)

\(⇒ s=(0\times t)+\frac{1}{2}at^{2}\)

\(⇒ s=\frac{1}{2}at^{2}\)

\(⇒ a=\frac{2s}{t^{2}}\)     -----(4)

By equation 1, equation 2, equation 3, and equation 4,

⇒  P = mav

\(⇒ P=\frac{maS}{t}\)

\(⇒ P=\frac{2mS^2}{t^3}\)

\(⇒ S^2=\frac{Pt^3}{2m}\)

⇒ S ∝ t3/2

  • Hence, option 3 is correct.

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