The position of a particle is given by
`r = 3t hati +2t^(2) hatj +8 hatk`
where, t is in seconds and the coefficients have the proper units for r to be in metres.
(i) Find v (t) and a(t) of the particles.
(ii) Find the magnitude and direction of v(t) and a(t) at `1 = 1s`.

Explanation

`v(t)=(dr)/(dt)=(d)/(dt)(3.0thati+2.0t^(2)hatj+5.0hatk)`
`=3.0hati+4.0thatj`
a `(t)=(dv)/(dt)=+4.0hatj`
`a=4.0 " m s"^(-2)` along y- direction
At t=1.0s, `v=3.0hati+4.0hatj`
It .s magnitude is `v=sqrt(3^(2)+4^(2))=5.0 " m s"^(-1)` and direction is
`theta=tan^(-1)((v_(y))/(v_(x)))=tan^(-1)((4)/(3))~=53^(@)` with x - axis.