Work Energy And Power Question 72
Question: A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to [IIT 1984; BHU 1984, 95; MP PET 1996; JIPMER 2000; AMU (Med.) 1999]
Options:
A) $ {t^{1/2}} $
B) $ {t^{3/4}} $
C) $ {t^{3/2}} $
D) $ t^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ P=Fv=mav=m( \frac{dv}{dt} )\ v $
therefore $ \frac{P}{m}dt=v\ dv $
therefore $ \frac{P}{m}\times t=\frac{v^{2}}{2} $
therefore $ v={{( \frac{2P}{m} )}^{1/2}}{{(t)}^{1/2}} $ Now $ s=\int _{{}}^{{}}{v\ dt=\int _{{}}^{{}}{{{( \frac{2P}{m} )}^{1/2}}{t^{1/2}}dt}} $ \ $ s={{( \frac{2P}{m} )}^{1/2}}[ \frac{2{t^{3/2}}}{3} ] $
therefore $ s\propto {t^{3/2}} $
