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))`.

Displacement (x) and time (t) of a particle in motion are related as x = at + bt^(2) -ct^(3) where a,b, and c, are constants. Velocity of the particle when its acceleration becomes zero is

The displacement (s ) of a particle depends on time (t) as s = 2at^(2)-bt^(3) . Then

Potential energy of a particle is 1/2momega^(2)x^(2) , where m and omega are constants. Prove that the motion of the particle is simple harmonic.

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 x and y coordiates of a particle at any time t are given by x = 7t + 14 t^(2) and y = 5t, where x and y are in metre and t is in second. The acceleration of the particle at t = 5 s is

The equation x= A sin omega t gives the relation between the time t and the corresponding displacement x of a moving particle where A and omega are constant. Prove that the acceleration of the particle is proportional to its displacement and is directed opposite to it.

The kinetic energy of a particle is 1/2momega^(2)(A^(2)-x^(2)) , where m, omega and A are constants. Prove that the motion of the particle is simple harmonic.

The magnetic flux linked with a coil varies with time t as phi=at^(2)+bt+c , where a, b and c are constants. The emf induced in the coil will be zero at a time of

The position vector vecr of a particle with respect to the origin changes with time t as vecr =Athati-Bt^2hatj, where A and B are positive constants. Determine (i) the locus of the particle,