A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of 1 m, starting from rest.
After traveling 1 m, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart?
##J = \Delta p = Favg \times \Delta t##
##\Delta x = (\Delta p \times \Delta t)/ m##
(from the equation for impulse and change in momentum: \Delta x / \Delta t = v_f because the carts start at rest)
##\Delta x = v_i \times \Delta t + .5 \times a_x \times \Delta t^2##
##\Delta x = .5 \times (v_i + v_f) \times \Delta t##
The Attempt at a Solution
I did algebra using delta x and tried both kinematics equations. The entire reason I posted this is because, using both kinematics equations, I derived the statement ##\Delta p = .5 \times \Delta p##. So I must have made a mistake somewhere but I can't figure out where. The acceleration is constant so I should be able to use the kinematics equations.
I think there are solutions to this problem on the Internet, but the main reason I posted this is because of the momentum equals half of itself solutions I got. But if someone wants to help me with the solution to the actual problem as well, that would be appreciated. I messed around with equations and tried to figure out the behavior of the two carts compared to each other, but wasn't yet able to find a solution to how they compare at 1 m.
edit: sorry for the messed up Latex before this edit, i had an appointment to go to so i didn't have time to fix it before i left after i saw it was wrong