In a game of pool, a ball of mass 0.223 kg is struck with an average force of 53.9 N in 11.5 ms. Find the spee

In a game of pool, a ball of mass 0.223 kg is struck with an average force of 53.9 N in 11.5 ms. Find the speed of the ball after it was struck.

This is an impulse problem. Recognize that impulse is the change in momentum as well as the force multiplied by elapsed time:

mΔv = FΔt

As the initial velocity is not given, assume that the ball is initially at rest (v1 = 0)

m(v2 - v1) = FΔt
v2 - 0 = FΔt / m
v2 = (53.9N)(11.5 * 10^-3 s) / (0.223 kg)
= 2.77959641 m/s

Rounding to three sig figs, the speed of the ball after it was struck is 2.78 m/s.

Let 'm' is the mass of the ball, 'F' is the average force with which ball is strucked, 'v1' is the initial speed of the ball, 'v2' is the final speed of the ball, 't' is the time and 'a' is the acceleration. Lets make data now:

m = 0.223 kg,
F = 53.9 N,
t = 11.5 ms = 11.5 * 10^-3 sec,
v1 = 0 (Because the ball is initially at rest),
v2 = ???

Solution:
Lets determine the acceleration first. Using Newton's 2nd law of motion, we have:

F = m a

=> a = F / m

=> a = (53.9) / (0.223)

=> a = 241.7 m/s^2

Now using first equation of motion:

v2 = v1 + a t

=> v2 = 0 + (241.7) (11.5 * 10^-3)

=> v2 = 2.77959 * 10^-6 m/s (ANSWER)

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