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)

the answer would be a