371754 A ball of mass \(0.45 \mathrm{~kg}\) which is initially at rest is hit by a bat. The bat remains in contact with the ball for \(3 \times 10^{-3} \mathrm{~s}\). During this time period the force on the ball by the bat is given as \(\mathbf{F}(\mathbf{t})=\left[\left(\alpha \times 10^{6}\right) \mathrm{t}-\left(\beta \times 10^{9}\right) \mathbf{t}^{2}\right] \mathrm{N}\) where \(\alpha\) and \(\beta\) are constants. The ball's speed, immediately as it loses contact with the bat is \(20 \mathrm{~m} / \mathrm{s}\). The correct relation between \(\alpha\) and \(\beta\) as
371754 A ball of mass \(0.45 \mathrm{~kg}\) which is initially at rest is hit by a bat. The bat remains in contact with the ball for \(3 \times 10^{-3} \mathrm{~s}\). During this time period the force on the ball by the bat is given as \(\mathbf{F}(\mathbf{t})=\left[\left(\alpha \times 10^{6}\right) \mathrm{t}-\left(\beta \times 10^{9}\right) \mathbf{t}^{2}\right] \mathrm{N}\) where \(\alpha\) and \(\beta\) are constants. The ball's speed, immediately as it loses contact with the bat is \(20 \mathrm{~m} / \mathrm{s}\). The correct relation between \(\alpha\) and \(\beta\) as
371754 A ball of mass \(0.45 \mathrm{~kg}\) which is initially at rest is hit by a bat. The bat remains in contact with the ball for \(3 \times 10^{-3} \mathrm{~s}\). During this time period the force on the ball by the bat is given as \(\mathbf{F}(\mathbf{t})=\left[\left(\alpha \times 10^{6}\right) \mathrm{t}-\left(\beta \times 10^{9}\right) \mathbf{t}^{2}\right] \mathrm{N}\) where \(\alpha\) and \(\beta\) are constants. The ball's speed, immediately as it loses contact with the bat is \(20 \mathrm{~m} / \mathrm{s}\). The correct relation between \(\alpha\) and \(\beta\) as
371754 A ball of mass \(0.45 \mathrm{~kg}\) which is initially at rest is hit by a bat. The bat remains in contact with the ball for \(3 \times 10^{-3} \mathrm{~s}\). During this time period the force on the ball by the bat is given as \(\mathbf{F}(\mathbf{t})=\left[\left(\alpha \times 10^{6}\right) \mathrm{t}-\left(\beta \times 10^{9}\right) \mathbf{t}^{2}\right] \mathrm{N}\) where \(\alpha\) and \(\beta\) are constants. The ball's speed, immediately as it loses contact with the bat is \(20 \mathrm{~m} / \mathrm{s}\). The correct relation between \(\alpha\) and \(\beta\) as