Difficult# Two Forces Acting on an Object: A Push-Me-Pull-You

APPHMC-VHAUV1

In the original Dr. Dolittle movie (from *20th Century Fox, 1967*) one of the strange animals is a Push-Me-Pull-You, which looks like a llama with two torsos, two pairs of front legs, and no hindquarters. (Don't ask how its digestive system works!)

Suppose that the two pairs of legs are not evenly matched, such that the left pair of legs can generate a force of ${F(t)}_{left}=(6\text{ N/s})t +1\text{ N}$ to the left, and the right pair of legs can generate a force of ${F(t)}_{right}=(4\text{ N/s})t +3\text{ N}$ to the right.

If the animal starts from rest, what is its momentum after $12$ seconds?