Question

The potential energy `U`(in `J`) of a particle is given by `(ax + by)`, where `a` and `b` are constants. The mass of the particle is `1 kg` and `x` and `y` are the coordinates of the particle in metre. The particle is at rest at `(4a, 2b)` at time `t = 0`.
Find the speed of the particle when it crosses y-axis.
A. `4 sqrt(a^(2) + b^(2))`
B. `2 sqrt(2 (a^(2) + b^(2)))`
C. `sqrt(2(a^(2) + b^(2)))`
D. `sqrt((a^(2) + b^(2)))`

Answer 1

Correct Answer - B
acceleration `|vec a_(x)|=-a,|vec a_(y)|=-b`
acceleration `|vec a| =sqrt(a_(x)^(2) + a_(y)^(2)) = sqrt(a^(2)+b^(2))`
`u_(x) =-at, v_(y) = -bt`
`X =4a+(1)/(2) a_(x)t^(2) =4a -(a)/(2)t^(2)`
`Y =2b+(1)/(2) a_(y)t^(2) =2b -(b)/(2) t^(2)`
particole crosses x-axis, when `y = 0`.