In total, the track is 120 ish cm long.
The carts themselves have length, though, so 120 cm, less the combined length of the two carts is only 87 cm. So when I center the two carts at the 60 cm, they are each 87cm / 2 = 43.5 cm away from the ends of the track.
How should the carts (0.5 kg and 1.0 kg are the masses) be positioned on the track if I still want them to arrive at opposite ends simultaneously?
Draw an IF chart to confirm your intuition. Consider that the velocities of both objects before they poosh off each other will be zero, which tells you a little something about the total Hodors/Junhees/Whatever6thHourDecidedToCallThem's. Write your prediction for the distances the carts should travel on a mini whiteboard, and compare to other groups....
Check out this video to confirm your suspicions.
Same goes for the 0.5 kg vs. 1.5 kg carts. How should the carts be positioned on the track if I still want them to arrive at opposite ends simultaneously?
Draw an IF chart to confirm your intuition. Consider that the velocities of both objects before they poosh off each other will be zero, which tells you a little something about the total Hodors/Junhees/Whatever6thHourDecidedToCallThem's.