Right answer is (a) π/60 s
The best explanation: Let the equation of motion be: x = 0.1sin(wt) where w is the angular frequency.
On derivating this equation w.r.t time we get: v = 0.1wcos(wt).
Given that maximum speed is 1m/s, we get 0.1w = 1.
∴ w = 10s^-1.
Now our equation of motion has become: x = 0.1sin(10t).
Assume we start from x=0 at t=0. Then by putting x=0.05 in the equation we can find the time. 0.05 = 0.1 sin(10t) ∴ sin(10t) = 0.5 ∴ 10t = π/6 ∴ t = π/60 s.