Exact energy triangles show how rest energy, pc, total energy, and kinetic energy move together. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Mass four at speed three totals one hundred twenty five joules
The first triangle uses mass 4 kg and speed 3 m/s. Rest energy is 100 J, motion leg pc is 75 J, and total energy is 125 J.
1002+752=1252K=125−100=25
Mass three at speed four reaches the same total another way
The second row lowers mass to 3 kg and raises speed to 4 m/s. Rest energy becomes 75 J, pc becomes 100 J, and the same total 125 J closes the triangle.
752+1002=1252K=125−75=50
Doubling the fast mass doubles every energy leg
Keeping speed 4 m/s and doubling mass to 6 kg doubles the second row: rest energy 150 J, pc 200 J, total 250 J, and kinetic energy 100 J.