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) 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

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 position vector of a particle is given by vec r = (2t hati+5t^(2)hatj)m (t is time in sec). Then the angle between initial velocity and initial acceleration is

The position vector of a particle P with respect to a stationary point O change with time according to the law vec(r) = vec(b) sin omega t + vec(c) cos omega t where vec(b) and vec(c) are constant vectors with b pot c and omega is a positive constant. Find the equation of the path of the particle y = f (x) , assuming x an dy axes to coincide with the direction of the vector vec(b) and vec(c) respectively and to have the origin at the point O

What is the angle between the v ectprs (vec A xx vec B) and (vec Bxx vec A) ?

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) .

A particle moving in the xy plane experiences a velocity dependent force vec F = k (v_yhati + v_x hat j) , where v_x and v_y are the x and y components of its velocity vec v . If vec a is the acceleration of the particle, then which of the following statements is true for the particle?