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=v2R ....(2)
where v is the speed of the particle.
From equation (1) and (2)
acos30o=v2R
⇒ 15cos30o=v22.5
⇒v=√32.5m/s=5.7m/s
Hence speed of the particle is 5.7m/s. Option D is correct