In the given figure, a=15m/s² represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R=2.5m at a given instant of time. The speed of the particle is:

Step 1: Centripetal acceleration [Ref. Fig.]
Total acceleration has two components, i.e. tangential acceleration(at) and centripetal acceleration(ac)
From the figure ac=acos30° (1)
Step 2: Speed calculation
Centripetal acceleration is given by ac=v²/R (2)
where v is the speed of the particle.
From equation (1) and (2)
ac cos30° = v²/R
→ 15cos30° = v²/2.5
→ v = √(3*2.5) m/s = 5.7m/s
Hence speed of the particle is 5.7m/s. Option D is correct