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

Given in the question, `v=t^(2)`
`therefore` Linear speed of particle at `t=2s` is `v=(2)^(2)=4ms^(-1)`
`therefore" Radial acceleration "a_(r)=(v^(2))/(r)=((4)^(2))/(2)=8ms^(-2)`
The tangential acceleration is `a_(t)=(dv)/(dt)=(d)/(dt)(t^(2))=2t`
`therefore` Tangential acceleration at t 2 s is
`a_(t)=(2)(2)=4ms^(-2)`
`therefore` Net acceleration of particle at t = 2 s is
`a=sqrt((a_(r))^(2)+(a_(t))^(2))=sqrt((8)^(2)+(4)^(2))=sqrt(64+16)" or "a=sqrt(80)"ms"^(-2)`