A particle of mass 3 kg takes 2 second to move from point A to B under the action of gravity and another constant force `vec(F)=(12hati-3hatj+12 hatk) N`, where the unit vector `hatk` is in the direction of upward vertical. The position vector of point B is `vec(r)_(B)=(15 hati-7hatj-6hatk)m` and velocity of the particle when it reaches B is `vec(V)_(B)=(12hati+hatj-4hatk m//s`.
(a) Find the velocity, `vec(V)_(A)`of the particle when it was at A.
(b) Find position vector, `vec(r)_(A)` of point A
(c) Find work done by the force `vec(F)` as the particle moves from A to B
(d) Find change in gravitational potential energy of the particle is it moves from A to B

Answer

(a) `vec(V)_(a)=(4hati+3hatj+2hatk) m//s`
(b) `vec(r)_(A)=(-hati+3hatj-4hatk) m`
(c) W=138 J
(d) `DeltaU_(g)=-60 J`