Using the conservation of momentum, the total initial momentum is equal to the total final momentum.

\(Initial momentum of P = 0.2 imes 0.5 = 0.1 ext{ kg m s}^{-1}\)

\(Initial momentum of Q = 0.3 imes (-1) = -0.3 ext{ kg m s}^{-1}\)

\(Total initial momentum = 0.1 - 0.3 = -0.2 ext{ kg m s}^{-1}\)

Let the speed of P after the collision be v. Since Q comes to rest, its final momentum is 0.

\(Total final momentum = 0.2 imes v + 0 = 0.2v\)

By conservation of momentum:

\(0.2v = -0.2\)

Solving for v gives:

\(v = -1 ext{ m s}^{-1}\)

Since speed is the magnitude of velocity, the speed of P after the collision is 1 m s^-1.