A particle moving in a straight line has velovity v given by `v^(2)=alpha-betay^(2)` , where `alpha` and `beta` are constants and y is its distance from a ficed point in the line. Show that the motion of particle is SHM. Find its itme period and amplitude.

A particular moving in a straight line has velocity v give by v^(2)=alpha-betay^(2) where alpha and beta are constant and y is its distance from a fixed point in the line . Show that the motion of the particle is SHM . Find its time period and amplitude.

A particle moves in a straight line so that its velocity at any point is given by v^(2)=a+bx , where a,b ne 0 are constants. The acceleration is

The instantaneous velocity of a particle moving in a straight line is given as v = alpha t + beta t^2 , where alpha and beta are constants. The distance travelled by the particle between 1s and 2s is :

A particle in moving in a straight line such that its velocity is given by v=12t-3t^(2) , where v is in m//s and t is in seconds. If at =0, the particle is at the origin, find the velocity at t=3 s .

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

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

A particle moves in a straight line as s =alpha(t-4)+beta(t-4)^(2) . Find the initial velocity and acceleration.