A body is projected up such that its position vector varies with time as `vecr = 6t hati+(8t-5t^2) hatj` . Find the initial velocity.

A body is projected up such that its position vector varies with time as vecr = 6t hati+(8t-5t^2) hatj . Find the time of flight.

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,

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 (ii) the nature of variation with time of the velocity and acceleration vectors, and also the moduli of them.

The position vector of a particle is, vecr=3thati-2t^2hatj+4hatk . Find out (i) its velocity vecv and acceleration veca ,

A particle moves in a straight line such that its distance x from a fixed point on it at any time t is given by x=1/4 t^4-2t^3+4t^2-7 . Find the time its velocity is maximum and the time when its acceleration is minimum.

The position vector of a particle is, vecr=3thati-2t^2hatj+4hatk . Find out (ii) the magnitude and direction of its velocity at t=2s.

Find the distance of the point with position vector 2 hati+ hatj- hatk from the plane vecr .( hati- 2 hatj+ 4 hatk)=9 .

A particle moves with uniform acceleration and the distance travelled in t - th second is s_(t) = 3 + 2t . Find the initial velocity of the particle .