A uniform rod of mass m and length l is struck at one end by a...

The impulse delivered to the rod is given by the product of the force and the time duration:

$J = Ft$

According to the impulse-momentum theorem, the net linear impulse applied to a system is equal to the change in its linear momentum. The point of application of the force affects the angular velocity but does not affect the linear velocity of the centre of mass.

$J = \Delta p_{cm}$

$Ft = m v_{cm} - 0$

$v_{cm} = \dfrac{Ft}{m}$