A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

Question

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) : (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

( dK / dE )= P = cos t ⇒ K = Pt =(1/2) mV 2 ∴ V =√(2 Pt / m )=( ds / dt ) ∴ S =√(2P / m ) (2/3) t (3/2)

Q. A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

$\frac{d K}{d E} = P = cos t$
$\Rightarrow K = Pt = \frac{1}{2} m V^{2}$
$∴ V = \frac{2 Pt}{m} = \frac{d s}{d t}$
$∴ S = \frac{2 P}{m} \frac{2}{3} t^{\frac{3}{2}}$

Q. A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

dEdK​=P=cost ⇒K=Pt=21​mV2 ∴V=m2Pt​​=dtds​ ∴S=m2P​​32​t23​

$\frac{d K}{d E} = P = cos t$
$\Rightarrow K = Pt = \frac{1}{2} m V^{2}$
$∴ V = \frac{2 Pt}{m} = \frac{d s}{d t}$
$∴ S = \frac{2 P}{m} \frac{2}{3} t^{\frac{3}{2}}$