Question

The potential energy U in joule of a particle of mass 1 kg moving the x-y plane obeys the law U = 3x + 4y, where (x, y) are the co-ordinates of the particle in meter. 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)

Answer 1

Answer: (A), (C), (D)

The correct options are
A

The particle has constant 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)

(A) $F_x=\frac{-dU}{dx}=-3$
$F_y=\frac{-dU}{dy}=-4\Rightarrow \overrightarrow{F}=-(3\hat{i}+4\hat{j})N$
(C) For particle to cross y-axis x = 0
$x=v_{x}t+\frac{1}{2}{a}_x{t}^2-6=0-\frac{1}{2}\times 3t^2\Rightarrow t=2sec$
For resultant velocity
$\overrightarrow{v}=0-(3i+4j)\times 2\Rightarrow |\overrightarrow{v}|=10m/s$

(D) $\Delta x=0-\frac{1}{2}\times 3\times 1^2=-1.5\Delta y=-0-\frac{1}{2}\times 4\times 1^2=-2$
Co - ordinate = (6 - 1.5, 4 - 2) = (4,5,2)