Mass m1 is has an initial velocity v1i. Mass m1 collides with a stationary mass m2. The net external force on the two particle system is zero. If the two masses stick together after the collision, then the final speed vf of the two masses is:

vf = (m1*v1i) / (m1 + m2)

Explanation:

take * as multiplication

from the conservation of linear momentum, we know that:

sum of pi = sum of pf, where sum of pi = m1*v1i + m2*v2i

pf = vf (m1 + m2) since the masses stick

together.

v2i = o, since mass m2 is initially stationary.

m1*v1i + m2 * (0) = vf (m1 + m2)

m1*v1i = vf (m1 + m2)

therefore

vf = m1*v1i / (m1 + m2)