Answer
$v = 4.2~m/s$
Work Step by Step
The impulse exerted on the ball by the cue stick is equal to the ball's change in momentum:
$mv = F~t$
$v = \frac{F~t}{m}$
$v = \frac{(24~N)(0.028~s)}{0.16~kg}$
$v = 4.2~m/s$
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