Question

A particle is released from rest at origin. It moves
under the influence of potential field U = x2-3x.
Its kinetic energy at x = 2 is
(1172 J
(2) 1.5 J
(3) 1 J
(4) Zero​

Answer 1

Answer:

u=x2-3x

Explanation:

du/dx=2x-3

x=2

du/dx =2(2)-3 =1J

Answer 2

answer : 2J

explanation : A particle is released from rest at origin.

so, initial velocity of particle , u = 0

potential potential of particle , U = x² - 3x

we have to find kinetic energy at x = 2.

we know,

force , F = - dU/dx

or, F = - d(x² - 3x)/dx = -(2x + 3)

or, F = 3 - 2x

as we know, F = ma = m(v dv/dx)

so, F = m(v dv/dx) = 3 - 2x

or, $m\int\limits^v_0{v}\,dv=\int\limits^2_0{(3-2x)}\,dx$

or, mv²/2 = $[3x-x^2]^2_0$

or, mv²/2 = 6 - 4 = 2J

as we know, kinetic energy = 1/2 mv²

so, kinetic energy = 2 J