1. Two carts, one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?

Answer 1

Force = change in momentum / change in time
if force the same and time the same
then
change in momentum the same (answer to first question)

f = m v /t
f = 2 m V /t
so
V = v/2

Ke of little mass = (1/2) m v^2
Ke of big mass = (1/2) 2m v^2/4
=(1/2)m v^2/2
so
Ke of big mass = 1/2 of Ke of little mass