The characteristic equation of a particle moving in a curved path are: `x=e^(-t), y=cos 3t` and `z=2 sin 3t,` where t stands for time. Find out
(i) Velocity and acceleration at any instant,

Explanation

Position vector of the particle at any instant,
`vecr=xhati+yhatj+zhatk=e^(-t)hati+2cos3t hatj+2sin 3thatk`
(i) Velocity , `vecv=(vec(dr))/(dt)=-e^(-t)hati-6sin 3t hatj+6 cos3thatk=-xhati-3zhatj+3yhatk`
Acceleration , `veca=(vec(dv))/(dt)=e^(-t)hati-18 cos3thatj-18sin3thatk=xhati-9yhatj-9zhatk`