A charged particle `(q,m)` is released from origin in an electric field `E = alpha - beta x` where `alpha` and `beta` are constants and `x` is distance from origin. Find the velocity of particle in terms of `x` and maximum displacement of the particle.

A particle of charge q and mass m moves rectilinearly under the action of an electric field E= alpha- beta x . Here, alpha and beta are positive constants and x is the distance from the point where the particle was initially at rest. Then: (1) the motion of the particle is oscillatory with amplitude (alpha)/(beta) (2) the mean position of the particles is at x= (alpha)/(beta) (3) the maximum acceleration of the particle is (q alpha)/(m) (4) All 1, 2 and 3

A particle starts from rest with acceleration a = alpha t + beta t^2 where alpha and beta are constants. Find its displacement between t = 1 and t= 2 second.

Energy due to position of a particle is given by, U=(alpha sqrty)/(y+beta) , where alpha and beta are constants, y is distance. The dimensions of (alpha xx beta) are

Energy due to position of a particle is given by, U=(alpha sqrty)/(y+beta) , where alpha and beta are constants, y is distance. The dimensions of (alpha xx beta) are