The velocity `upsilon` of a particle as a function of its position (x) is expressed as `upsilon = sqrt(c_(1)-c_(2)x)`, where `c_(1)` and `c_(2)` are positive constants. The acceleration of the particle is

A particle moves in the plane x y with constant acceleration a directed along the negative y-axis. The equation of motion of the particle has the form y = k_(1)x-k_(2)x^(2) , where k_(1) and k_(2) are positive constants. Find the velocity of the particle at the origin of coordinates.

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 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 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 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

The displacement x of a particle in rectilinear motion at time t is represented as x^(2) = at^(2) +2bt+c , where a ,b, and c are constants. Show that the acceleration of this particle varies (1)/(x^(3)) .

The displacement x of a particle at time t moving along a straight line path is given by x^(2) = at^(2) + 2bt + c where a, b and c are constants. The acceleration of the particle varies as

The velocity v of a particle is related to time t as v = 4+2 (c_(1)+c_(2)t) , where c_(1) and c_(2) are constants . Find out the initial velocity and acceleration.

The velocity of a particle moving along the positive direction of x-axis is v= Asqrt(x) , where A is a positive constant. At time t = 0 , the displacement of the particle is taken as x = 0 . (i) Express velocity and acceleration as functions of time , and (ii) find out the average velocity of the particle in the period when it travels through a distance s ?