A ball of mass  $0.45kg$ which is initially at rest is hit by a bat. The bat remains in contact with the ball for $3\times {10}^{-3}s.$ During this time period, the force on the ball by the bat varies with time t(in s) as  $F\left(t\right)=[(\alpha \times {10}^6)t-(\beta \times {10}^9)t^2]N$ where $\alpha$ and $\beta$ are constants. The ball's speed, immediately as it loses contact with the bat is 20 m/s. If the relation between  $\alpha$ and  $\beta$ is  $\alpha -2\beta =n,$ find  n.