What you're seeing
Impulse tab: a cart rolls, a force pushes on it for a set time, then it rolls on. The red arrow is the force. The arrow above the cart is its velocity. The bar is its momentum (mass × velocity).
Collisions tab: two carts roll toward each other, hit, and stick. Each bar is one cart's momentum. The green bar is the total. Watch the green bar during the crash.
Right is positive. A negative velocity means the cart is moving left.
Things to try
Run "Speed up: gentle" and then "Speed up: hard." The force and time are very different. Compare the final speeds.
Run the two "Slow down" examples. Which one is like an airbag? Which is like hitting a dashboard?
In Collisions, make the right cart heavy and slow, then light and fast. Can you make the stuck carts stop dead?
Switch to Full to see the force–time graph. The shaded area is the impulse.
What this leaves out
No friction or air drag, so carts keep rolling. Pushes are a constant force that switches on and off; real pushes ramp up and down. Collisions happen instantly, so you don't see the carts squash.