The potential energy of a particle of mass 5 kg moving in xy-plane is given as `U=(7x + 24y)` joule, x and y being in metre. Initially at `t=0`, the particle is at the origin `(0,0)` moving with velovity of `(8.6hati+23.2hatj) ms^(1)`, Then

Options

A. the magnitude of velocity of the particle at t=4 sec is 25 m/s
B. the magnitude of acceleration of the particle is `5 m//s^(2)`
C. the direction of motion of the particle initially at t=0 is at right angles to the direction of acceleration
D. the path of the particle is a circle.

Answer

ABC

Explanation

`V=-7xxx 24 y`
`F=(-dV)/(dx)=7hati-24 hatj`
`vec(a)=1/5(7hati-24hatj)`
`vec(u)=6(24hati+0.7 hatj)`
`vec(v)=vec(u)+vec(a)t=20 hati-15 hatj`
`(C) vec(u).vec(a)=0 ("so " 90^(@))`
(D) const. `vec(a)` so cannot be circle.