A particle of mass "2kg" is subjected to a two dimensional conservative force given by,F(X)=-2x+2y,F(y)=`2x-y^(2) `x,y in m and F in "N".If the particle has kinetic energy of "(8/3)J" at point "(2,3)" find the speed of the particle when it reaches "(1,2)" in "(m/s)" .

A conservative force F(x) act on a 1kg particle. The potential energy U(x)=(x-4)^(2) , At x=5 ,particle has kinetic energy of 24J .The greatest value of x to which particle can move is

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^(2)y-y^(3))AA x,y in R and f(1)=2 ,then

The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U=(-7x+24y)J , where x and y are given in metre. If the particle starts from rest, from the origin, then the speed of the particle at t=2 s is

A particle of mass of mass m = 1 kg is lying on x-axis experiences a force given by F = x(3x-2) Newton, where x is the x-coordinate of the particle in meters. The points where the particle is in equilibrium are-

The potential energy of a particle of mass 1 kg free to move along x-axis is given by U(x) =(x^(2)/2-x) joule. If total mechanical energy of the particle is 2J then find the maximum speed of the particle. (Assuming only conservative force acts on particle)

A single conservative force F(x) acts on a 1.0-kg particle that moves along the x-axis. The potential energy U(x) is given by U(x)=20+(x-2)^2 where x is in meters. At x=5.0m , the particle has a kinetic energy of 20J . The maximum kinetic energy of the particle and the value of x at which maximum kinetic energy occurs are

A single conservative f_((x)) acts on a m = 1 kg particle moving along the x-axis. The potential energy U_((x)) is given by : U_((x)) = 20 + (x - 2)^(2) where x is in metres. At x = 5 m , a particle has kintetic energy of 20 J The maximum speed of the particle is:

A single conservative f_((x)) acts on a m = 1 kg particle moving along the x-axis. The potential energy U_((x)) is given by : U_((x)) = 20 + (x - 2)^(2) where x is in metres. At x = 5 m , a particle has kintetic energy of 20 J The minimum speed of the particle is:

If the potential energy function of a particle is given by U=-(x^2+y^2+z^2) J, whre x,y and z are in meters. Find the force acting on the particle at point A(1m,3m,5m) .

A single conservative f_((x)) acts on a m = 1 kg particle moving along the x-axis. The potential energy U_((x)) is given by : U_((x)) = 20 + (x - 2)^(2) where x is in metres. At x = 5 m , a particle has kintetic energy of 20 J The position of equilibrium and its nature is: