Question

A particle moves so that its coordinates vary with time as x=`alpha sin omegat,y=alpha cos omegat` and `z=bt^(2)`. Find the initial:
(a) position (b) velocity (c) acceleration of the particle.

Answer 1

The initial position is
`vecr_(0)=[a sin omegathati+alpha cos omegathatj+bt^(2)hatk]_(t=0)=alphahatj`
(b) The speed of the particle at t=0 is
`v_(0)=[(dx)/(dt)hati+(dy)/(dt)hatj+(dz)/(dt)hatk]_(t=0)`
=`[-alphaomega^(2)sin omegat hati-alphaomega^(2) cos omegathatj+2bhatk]_(t=0)`
`=alphaomega^(2)hatj+2bhatk`