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

D

co-ordinates of particle at `t = 1 s` are `(4.5,2)`.

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`vec F -(du)/(dx) hat i -(du)/(dy) hat j , = -3 hati - 4 hat j`
`vec a = -a hat i - 4 hatj ,|vec a|=5`
on `y` axis `x = 0`, after time `t` sec. the particle crosses `y` axis.
`0-6=1//2 xx(-3_t)t^(2),t=2.v_(x)=(-3)xx2 =-6`
`v_(y)=(-4)xx 2=-8.|vec v|= 10 m//s`.
`t = 1 sec., x = 6 - 1//2 x 3 = 4.5`
`y = 4- 1//2 x 4 = 2`.
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