A) t3/4
B) t3/2
C) \[\sqrt{t}\]
D) t
Correct Answer: B
Solution :
Key Idea: Power is defined as amount of work done per unit time. Power is defined as time rate of doing work i.e., \[P=\frac{dW}{dt}\] Also work down = force \[\times \] displacement = F. d and force = mass \[\times \] acceleration = ma \[\therefore \] \[P=\frac{Fd}{t}=\frac{ma.d}{t}\] Also, distance = speed \[\times \] time i.e., \[d=vt\Rightarrow v=\frac{d}{t}\] and acceleration, \[a=\frac{v}{t}\] \[\therefore \] \[P=\frac{m}{{{t}^{2}}}vd\] \[P=\frac{m}{{{t}^{2}}}.\frac{d}{t}.d=\frac{m{{d}^{2}}}{{{t}^{3}}}\]\[\Rightarrow \] \[{{d}^{2}}\propto {{t}^{3}}\] \[\Rightarrow \] \[d\propto {{t}^{3/2}}\]
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