Question

Two identical carts travel at the same speed toward each other, and then a collision occurs. The graphs show the momentum of each cart as a function of time, both before and after the collision.

Which graph shows a perfectly inelastic collision?

There is a graph with time in seconds on the x axis and the y axis is labeled P in kilogram meters per second. There is a red horizontal line that drops down below the x axis and is the farther away from the x axis and a horizontal line. A blue line is the mirror image starting below the x axis and ending above the x axis. The red line is labeled car A and a blue line labeled car B. At the point both graphs cross the x axis is labeled collision.
A graph with momentum on the y axis measured in kilogram meters per second and time on the x axis measured in seconds. There are no values on the axes. There are two curves on the graph. The first starts above the x axis and is horizontal before curving downward to the x axis labeled 2 m cart. The second curve starts below the axis, the same distance below as the first one was above, and is horizontal before curving upward toward the x axis at the same time and labeled m cart. Where they meet is labeled Collision. Both curves meet at the x axis at the same time and are both on the x axis for a time period labeled Combined carts.
A graph with momentum on the y axis measured in kilogram meters per second and time on the x axis measured in seconds. There are no values on the axes. There are two curves on the graph the first starts above the x axis and is horizontal before curving downward toward the x axis labeled 2 m cart. The second curve starts below the axis, a smaller distance below as the first one was above, and is horizontal before curving upward toward and crosses the x axis and is labeled m cart. Where they meet is labeled Collision. Both curves meet above the axis at the same time and both go horizontal above the x axis for a time period labeled Combined carts.
There is a graph with time in seconds on the x axis and the y axis is labeled P in kilogram meters per second. There is a red horizontal line that drops down below the x axis and is then farther away from the x axis and a horizontal line. A blue line is the mirror image starting below the x axis and ending above the x axis. The red line is labeled car A and a blue line labeled car B. At the point both graphs cross the x axis is labeled collision.

Answer 1

The second graph — the one where each cart's momentum drops to zero at the collision and both remain at zero (both curves meet on the x‑axis and stay there).

Reason: two identical carts moving toward each other have equal and opposite momenta so the total momentum is zero. In a perfectly inelastic collision they stick together, so the combined mass must have zero velocity (to conserve momentum), hence zero momentum after the collision. That matches the graph where both momenta go to and stay at zero.