Consider two carts moving on a track. The first cart has a mass of m$,$ and the second cart has a mass of $3$m$.$ The first mass is moving at a velocity v towards the second, which is stationary.

$$

After the collision, the first cart is observed moving away from the second at a velocity of v$/2.$ How much impulse did the second cart transfer to the first?

$3/2$mv$1/2$mvZero, the direction of impulse transfer was towards the heavy cart, not towards the light cart$\mathrm{.}2$mvZero, the heavier cart is stationary and has no momentum to transfer to the lighter one.