Position of particle as a function of time is given as `vec r=cos wt hati+sin wt hatj` . Choose correct statement about `vecr,vec v` and `vec a` where `vec v` and `vec a` are velocity and acceleration of particle at time t.

The position of a particle is given by vec r =(8 t hati +3t^(2) +5 hatk) m where t is measured in second and vec r in meter. Calculate, the magnitude of velocity at t = 5 s,

The position of a particle is given by vec r =(8 t hati +3t^(2) +5 hatk) m where t is measured in second and vec r in meter. Calculate, the magnitude of velocity at t = 5 s,

The position of a particle is given by vec r =(8 t hati +3t^(2) hatj +5 hatk) m where t is measured in second and vec r in meter. Calculate, direction of the velocity at t = 1 s

The position of a particle is given by vec r =(8 t hati +3t^(2) hatj +5 hatk) m where t is measured in second and vec r in meter. Calculate, direction of the velocity at t = 1 s

The position vector of a particle is vec( r) = a cos omega t i + a sin omega t j , the velocity of the particle is

State the direction of velocity of a particle with position vector given by bar r = {a cos wt} hati + a sin wt hatj .

A system of particles is free from any external force vec v and vec a be the velocity and acceleration of the centre of mass, then it necessarily follows that :

The velocity of a particle varies with time as per the law vec(V) = vec(a) + vec(b)t where vec(a) and vec(b) are two constant vectors. The time at which velocity of the particle is perpendicular to velocity of the particle at t= 0 is

A particle travels so that its acceleration is given by vec(a)=5 cos t hat(i)-3 sin t hat(j) . If the particle is located at (-3, 2) at time t=0 and is moving with a velocity given by (-3hat(i)+2hat(j)) . Find (i) The velocity [vec(v)=int vec(a).dt] at time t and (ii) The position vector [vec(r)=int vec(v).dt] of the particle at time t (t gt 0) .