A particle moves on a circle of radius `r` with centripetal acceleration as function of time as `a_c = k^2 r t^2`, where `k` is a positive constant. Find the following quantities as function of time at an instant :
(a) The speed of the particle
(b) The tangential acceleration of the particle
( c) The resultant acceleration, and
(d) Angle made by the resultant with tangential direction.

Options

A. `kt^(2)`
B. `kr`
C. `krsqrt(k^(2)t^(4)+1)`
D. `krsqrt(k^(2)t^(2)-1)`

Answer

C

Explanation

From given eqution `omega=kt`,
`alpha=(domega)/(dt)=k,a_(t)=ra,a=sqrt(a_(c)^(2)+a_(t)^(2))`