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.

A particle is moving along a straight line path according to the relations s^(2)=at^(2)+2bt+c represent the distance travelled in t seconds and a, b, c are constant. Then the acceleration of the particle varies as:

The distance traversed by a moving particle at any instant is half of the product of its velocity and the time of travers. Show that the acceleration of particle is constant.

A particle is travelling along a straight line OX. The distance r of the particle from O at a timet 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

If the distance s travelled by a particle in time t is s=a sin t +b cos 2t , then the acceleration at t=0 is

A particle moves along a straight line on y-axis. The distance of the particle from O varies with time and is given by : y = 20t - t^2 . The distance travelled by the particle before it momentarily comes to rest is

A particle moves along a straight line on y-axis. The distance of the particle from O varies with time and is given by : y = 20t - t^2 . The distance travelled by the particle before it momentarily comes to rest is

A particle at rest is moved along a straight line by a machine giving constant power. The distance moved by the particle in time 't' is proportional to

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)) .

If a particle moving in a straight line and its distance x cms from a fixed point O on the line is given by x=sqrt(1+t^(2)) cms, then acceleration of the particle at t sec. is

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