You need to be able to work these problems where you have the a vs. t. You find the accumulation of area of the a vs. t. This gives you where the v vs. t ends up. Then you find the v vs. t accumulation area and that tells you where the final x position is. On the Take Home Test, the final x position (area of the right triangle of v vs. t) tells you the final position which is the length of the gun barrel.