In the given figure, a = 15m s ^ - 2 represents the total...

Centripetal acceleration is the radial component of resultant acceleration.

Referring the figure in question, radial component of the resultant acceleration,

$= 15\cos 30 ° = 15 \times \dfrac{\sqrt{3}}{2}$

$⇒ \dfrac{{v}^{2}}{r} = 15 \times \dfrac{\sqrt{3}}{2}$

$⇒ v = \sqrt{15 \times \dfrac{\sqrt{3}}{2} \times 2 . 5} ≃ 5 . 7m{s}^{- 1}$.