The position error constant (Kp) for the given transfer function G(s) is 5, while the speed (Kv) and acceleration (Ka) error constants are both 0.
The position, speed, and acceleration error constants for a system with transfer function G(s) = \frac{10}{(s+1)(2s+1)} can be determined through the final value theorem using the system type and the presence of poles at the origin. In this case, there are no poles at the origin, and therefore the system is of type 0.
The position error constant (Kp) is the static gain of the system, which is given by G(0) = \frac{10}{1 \cdot 2}. The speed error constant (Kv) and acceleration error constant (Ka) for a type 0 system are zero, as these constants require at least one or two integrators (poles at the origin) respectively, to be non-zero.
So, the position error constant is 5 (the static gain), while the speed and acceleration error constants are both 0 for this system.