The acceleration `(a)` of an object varies as a function of its velocity `(v)` as `a=lambda sqrt(v)` where `lambda` is a constant.If at t=0,v=0, then the velocity as a function of time `(t)` is given as

A point moves along an arc of a circle of radius R . Its velocity depends on the distance s covered as v=lambdasqrt(s) , where lambda is a constant. Find the angle theta between the acceleration and velocity as a function of s .

A particle moves with an initial velocity V_(0) and retardation alpha v , where alpha is a constant and v is the velocity at any time t. Velocity of particle at time is :

Calculate the acceleration of an object if its velocity is given by v= ( sqrt(12t -2)) .

A particle is moving in a straight line such that its velocity varies as v=v_(0) e^(-lambdat) , where lambda is a constant. Find average velocity during the time interval in which the velocity decreases from v_(0) to v_(0)/2 .

A particle moves with an initial velocity V_(0) and retardation alpha v , where alpha is a constant and v is the velocity at any time t. total distance covered by the particle is

A particle moves with an initial velocity v_(0) and retardation alphav, where alpha is a constant and v is the velocity at any time t. If the particle is at the origin at t=0 , find (a) (i) velocity as a function of time t. (ii) After how much time the particle stops? (iii) After how much time velocity decreases by 50% ? (b) (i) Velocity as a function of displacement s. (ii) The maximum distance covered by the particle. (c ) Displacement as a function of time t.

A particle moves with an initial velocity V_(0) and retardation alpha v , where alpha is a constant and v is the velocity at any time t. After how much time, speed of particle decreases by 75%

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 acceleration of a particle travelling along a straight line is a =(k)/(v) , where k is constant (k gt 0) . If at t=0,V=V_(0) then speed of particle at t = (V_(0)^(2))/(2) .