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The potential energy U in joule of a par...

The potential energy `U` in joule of a particle of mass `1 kg` moving in `x-y` plane obeys the law`U = 3x + 4y`, where `(x,y)` are the co-ordinates of the particle in metre. If the particle is at rest at `(6,4)` at time `t = 0` then :

A

the particle has constant acceleration

B

the particle has zero acceleration

C

the speed of the particle when it crosses y-axis is `10 m//s`

D

co-ordinate of particle at `t = 1` sec is (4.5, 2)

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The correct Answer is:
A, C, D
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Knowledge Check

  • The potential energy varphi , in joule, of a particle of mass 1kg , moving in the x-y plane, obeys the law varphi=3x+4y , where (x,y) are the coordinates of the particle in metre. If the particle is at rest at (6,4) at time t=0 , then

    A
    (a) The particle has constant acceleration.
    B
    (b) The work done by the external forces, the position of rest of the particle and the instant of the particle crossing the x-axis is `25J`.
    C
    (c) The speed of the particle when it crosses the y-axis is `10m^-1`.
    D
    (d) The coordinates of the particle at time `t=4s` are `(-18,-28)`.

  • The potential energy phi in joule of a particle of mass 1 kg, moving in the x-y plane, obeys the law, phi = 3x + 4y , where (x,y) are the corrdinates of the particle in meter. If the particle is at rest at (6, 4) (in m) at time t = 0 , then :

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    The work done by external forces from the position of rest to the instant the particle crossing x-axis is `25J`
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  • The potential energy phi in joule of a particle of mass 1 kg moving in x-y plane obeys the law, phi=3x + 4y . Here, x and y are in metres. If the particle is at rest at (6m, 8m) at time 0, then the work done by conservative force on the particle from the initial position to the instant when it crosses the x-axis is .

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    `25 J`
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    `25 J`
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    D
    `-50 J`

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