# Linear momentum of two particles

## Homework Statement

Two particles of different mass start from rest. The same net force acts on both of them as they move over equal distances. How do the magnitudes of their final momenta compare?

The particles have equal momenta.
b. The particle of smaller mass has more momentum.
c. The particle of larger mass has more momentum.
d. Either particle might have more momentum.

## The Attempt at a Solution

Ok I started by working out the kinetic energy for both particles would be equal.. Force x Distance.

Now from this It would make sense to me that the lighter particle would have a higher velocity over distance, due to V^2 in 1/2MV^2. So if we look at momentum, MV, it would be greater for the smaller mass? Noting the mass is less, but the Velocity has been squared.

I'll give it a shot...
OK, so you figured out that the change in kinetic energy for both particles is equal. Let's call the heavier mass M and its velocity V, and call the lighter mass m and its velocity v. So Kinetic energy of (M) = Kinetic energy of (m). In other words:

1/2 * M * V^2 = 1/2 * m * v^2

the 1/2 cancels, and we're left with MV^2 = mv^2
Let's solve for v. Divide both sides by m and take square root:

√(M/m) * V = v

OK, now you have enough information to compare the momentum equation and see which one is greater.