A particle moves in a circle of radius `2 cm` at a speed given by `v = 4t`, where `v` is in `cm s^-1` and `t` is in seconds.
(a) Find the tangential acceleration at `t = 1 s`
(b) Find total acceleration at `t = 1 s`.

Explanation

Given, v = 4t
Radial acceleration,
`a_(r)=(v^(2))/(R)=((4t)^(2))/(R)" or "a_(r)=(16r^(2))/(2)=8t^(2)`
At t = 1 s, `a_(r)=8cms^(-2)`
(i) Tangential acceleration,
`a_(t)=(dv)/(dt)`
or `a_(t)=(d)/(dt)(4t)=4cms^(-2)`
i.e., `a_(t)` is constant or tangential acceleration at t = 1 s is `4cms^(-2)`.
Total acceleration, `a=sqrt(a_(t)^(2)+a_(r)^(2))`
or `a=sqrt((4)^(2)+(8)^(2))=sqrt(80)=sqrt3cms^(-2)`