Bill and Tom are both towing wagons. Bill's wagon weighs 10 pounds, and Tom's wagon weighs 20 pounds. Bill is pulling his wagon with twice the force that Tom is. How do the wagon speeds compare?

To compare speeds speeds of wagons we will use second Newton's law. It states:

F = m * a

Here we can see that force depends on the acceleration. If we know acceleration for both wagons we can compare them to make conclusion of speeds of wagons.

We have:

m1 = 10lb

m2 = 20lb

F1 = 2*F2

Also:

m2 = 2*m1

For Bill we have equation:

F1 = m1 * a1

For Tom we have equation:

F2 = m2 * a2

After inserting identities we have:

2*F2 = m1 * a1

F2 = 2*m1 * a2

In order to make conclusions about speeds we will solve these equations for a and find their ratio:

a1 = 2F2 / m1

a2 = F2 / 2m1

a1 / a2 = (2F2/m1) / (F2/2m1)

a1 / a2 = (2F2*2m1) / (m1*F2)

a1 / a2 = (4F2m1) / (m1F2)

a1 / a2 = 4

This ratio is bigger than 1 and this means that a1 is greater than a2. a1 is 4 times greater than a2. Speed of Bill's wagon is 4 times greater than speed of Tom's wagon.