JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Work, Power & Energy

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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 (graph are drawn schematically and are not to scale):

(A)(see structure)
(B)(see structure)
✓ Correct
(C)(see structure)
(D)(see structure)

Answer: (B)

Solution

Constant power means

P = F v

stays fixed, and by the work-energy theorem

P t = \frac{1}{2} m v^{2}

, so

v = \frac{2 P t}{m} \propto t

. Since

v = \frac{d s}{d t} \propto t^{1/2}

, integrating gives

s \propto t^{3/2}

. The displacement therefore leaves the origin with zero slope and curves steadily upward with ever-increasing slope, the concave-up growth that matches the described graph.

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option

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