The speed of a particle moving in a circle of radius `r=2m` varies witht time `t` as `v=t^(2)`, where `t` is in second and `v` in `m//s`. Find the radial, tangential and net acceleration at `t=2s`.

Explanation

`"Radial acceleration "a_(r)=(v^(2))/(r )=((4)^(2))/(2)=8m//s^(2)`
The tangential acceleration is `a_(t)=(dvecv)/(dt)=2t`
So, tangential acceleration at `t=2s` is
`a_(t)=(2)(2)=4m//s^(2)`
Net acceleration of particle `t:=2s` is
`a=sqrt(8^(2)+4^(2))=sqrt(80)m//s^(2)`