A particle undergoes one dimensional motion such that its velocity varies according to relation `v(x)=alpha x^(-2m)` where a and m are positive constants and x is the position of the particle. The ratio of acceleration to the velocity for m=1 varies with position x as

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = beta x^(-2 n) where beta and n are constant and x is the position of the particle. The acceleration of the particle as a function of x is given by.

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = beta x^(-2 n) where beta and n are constant and x is the position of the particle. The acceleration of the particle as a function of x is given by.

A particle of unit mass is moving along x-axis. The velocity of particle varies with position x as v(x). =alphax^-beta (where alpha and beta are positive constants and x>0 ). The acceleration of the particle as a function of x is given as

A particle is executing SHM and its velocity v is related to its position (x) as v^(2) + ax^(2) =b , where a and b are positive constant. The frequency of oscillation of particle is

A particle moves in a circular path such that its speed v varies with distance as V= alphasqrt(s) where alpha is a positive constant. Find the acceleration of the particle after traversing a distance s.

A particle located in one dimensional potential field has potential energy function U(x)=(a)/(x^(2))-(b)/(x^(3)) , where a and b are positive constants. The position of equilibrium corresponds to x equal to

A particle located in a one-dimensional potential field has its potential energy function as U(x)(a)/(x^4)-(b)/(x^2) , where a and b are positive constants. The position of equilibrium x corresponds to

The velocity varies with time as vecv = ahati + bthatj , where a and b are positive constants. The magnitude of instantaneous velocity and acceleration would be

A particle moves in the x-y plane according to the law x=at, y=at (1-alpha t) where a and alpha are positive constants and t is time. Find the velocity and acceleration vector. The moment t_(0) at which the velocity vector forms angle of 90^(@) with acceleration vector.

A particle moving in a straight line has its velocit varying with time according to relation v = t^(2) - 6t +8 (m//s) where t is in seconds. The CORRECT statement(s) about motion of this particle is/are:-