A particle at `t = 0` second is at point `A` and moves along the shown path (ABCDF) with uniform speed `v = (1 + (pi)/(3)) m//s`. Both the straight segments `AB` and `DE` are along the diameter `BD` of semicircle `BCD` radius `R = 1` meter. Find the instant of time at which the instantaneous velocity of the particle is along the direction of average velocity from `t = 0` second to that instant.

Options

A. 2 sec
B. 4 sec
C. 1 sec
D. 1.5 sec

Answer

C

Explanation

The required condition is achieved when the particle is at `P` such that `AP` is tangent to semicircle.
Hence required time `= (R+(R pi)/(3))/(v) = 1 sec`.