The energy-momentum relation is drawn here as a right-triangle ledger: rest energy is one leg, momentum times the speed limit is the motion leg, and total energy closes the hypotenuse. With momentum 15 kg m/s and toy speed limit 5 m/s, the motion leg is 75 J, which fits with rest energy 100 J and total energy 125 J. Real checks need consistent units, frame choice, measured momentum, calibrated energy, and uncertainty rather than just the neat toy triangle.
The same momentum closes an exact energy-momentum right triangle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Momentum times speed limit is the motion leg
Momentum 15 kg m/s times speed limit 5 m/s gives motion-energy leg 75 J.
15⋅5=75
Energy and momentum close a right triangle
The total energy 125 J closes with motion leg 75 J and rest leg 100 J.