O is fixed point on the straight line traced out by a moving particle. If the distance of the particle from O at time t be `(a cos nt + b sin nt ) ` [ a,b and n are constants]., show that the acceleration of the particle varies as its distance from O.

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)) .

A particle crosses points A, B, C in a straight line at a constant acceleration. The particle travels from A to B in time t_(1) and B to C in time t_(2) . If AB = a , BC = b then prove that the acceleration of the particle is 2(bt_(1)-at_(2))//t_(1)t_(2)(t_(1)+t_(2)) .

A particle is travelling along a straight line OX. The distance x (in metres) of the particle from O at a time t is given by x=37+27t-t^(3) where t is time in seconds. The distance of the particle from O when it comes to rest is

A particle starts from the origin and moves along a straight line. If the velocity of the particle at time t seconds be 10t cm/s, find the distance traversed during first 4 seconds after the start.

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.

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

A particle is moving in a straight line. At time, the distance between the particle from its starting point is given by x=t-6t^(2)+t^(3) . lts acceleration will be zero at

A particle starts moving from rest from a fixed point in a fixed direction. The distances from the fixed point at a time t is given by s= t^(2)+at-b+17 , where a, b are real numbers. If the particle comes to rest after 5 sec at a distance of s = 25 units from the fixed point, then values of a and bare respectively