Kinematics

JEE Main level, single correct, medium

31 of 308

Question 31 of 308

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time tt is proportional to:

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Answer: (A) t32{t}^{\dfrac{3}{2}}

P=P= constant
12mv2=Pt\dfrac{1}{2}m{v}^{2}=Pt
⇒v∝t\Rightarrow v\propto \sqrt{t}
dxdt=Ct\dfrac{dx}{dt}=C\sqrt{t} C=C= constant
by integration,
x=Ct12+112+1x=C\dfrac{{t}^{\dfrac{1}{2}+1}}{\dfrac{1}{2}+1}
x∝t3/2x\propto {t}^{3/2}

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