a particle moves on a circular path of radius 8 m. distance traveled by the particle in time t is given by the equation `s=2/3 t^(3)`. Find its speed when tangential and normal accelerations have equal magnitude.

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `3:1`

Answer

B

Explanation

The ratio of tangential to centripetal acceleration is
`((a_(t))/(a_(c)))_(t=t)=((dv)/(dt))/((v^(2))/(r))=((d)/(dt)((ds)/(dt)))/((ds)/(dt))^(2)t=((d)/(dt)(6t^(2)))/(6t^(2))^(2)r=((12t)xx12)/(36t^(4))=(4)/(t^(3))`
`therefore" "((a_(t)^(.))/a_(c))_(t=2z)=(4)/((2)^(2))=(1)/(2)`