Correct Answer - Option 3 : t
3/2
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
⇒ 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.