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Q.

The potential energy ϕ in joule of a particle of mass 1 kg moving in the x – y plane, obeys the law φ = 3x + 4y , where (x, y) are the coordinate of the particle in metre. If theparticle is at rest at (6, 4) at time t = 0, then (only conservative force are acting on particle).

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a

the particle has constant acceleration

b

the work done by the conservative forces from position of rest of the particle to the instant of the particle crossing x axis is 25 J

c

the speed of the a particle when it crosses the y axis is 52ms–1

d

the coordinates of the particle at time t = 4s are (–18, –28)

answer is A.

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Detailed Solution

F→=(3i^−4 )N,Wcon.f =Ui−Uf=(34−9) J=25J & 12mv2+9=34 ⇒v=52  m/s
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