A 4 kg wagon rolls at 5 m/s. Its kinetic energy: half the mass is 0.5 × 4 = 2, the speed squared is 5 × 5 = 25, and 2 × 25 = 50, so 50 J.
Now the same wagon rolls twice as fast. Double the speed: does that just double the joules?
Run the count again at 10 m/s, same wagon.
The speed squared is now 10 × 10 = 100, and 2 × 100 = 200, so 200 J.
The speed doubled. The kinetic energy went from 50 J to 200 J: four times as much.
The reason sits in the equation. The speed enters KE = ½mv² squared, so doubling v multiplies v² by 4.
Tripling the speed multiplies the kinetic energy by 3 × 3 = 9.
For the same wagon that is 50 × 9 = 450: tripled speed takes it from 50 J to 450 J.
This is why modest speed differences carry outsized energy differences.
A radio-controlled car carries 32 J of kinetic energy at 6 m/s. Its speed rises to 12 m/s and its mass stays the same. Enter its new kinetic energy in J.
A model train carries 12 J of kinetic energy at 1 m/s. Its speed rises to 3 m/s, mass unchanged. Calculate its new kinetic energy.
The speed is multiplied by 3.
The kinetic energy is multiplied by 3 × 3 = 9.
KE = 12 × 9 = 108
The train's new kinetic energy is 108 J.
A city bus carries 2800 J of kinetic energy approaching a stop. Its speed halves, mass unchanged. Calculate its new kinetic energy.
The speed is multiplied by 0.5.
The kinetic energy is multiplied by 0.5 × 0.5 = 0.25.
KE = 2800 × 0.25 = 700
The bus's new kinetic energy is 700 J.
Romy says: 'If a van's speed triples while its mass stays the same, its kinetic energy becomes nine times as large.' Is Romy correct?
Soren says: 'Doubling a cyclist's speed doubles her kinetic energy.' Is Soren correct?
A courier bike carries 180 J of kinetic energy at 5 m/s. Running late, the courier triples the speed to 15 m/s, mass unchanged. Enter the new kinetic energy in J.
A delivery drone's speed doubles, its mass unchanged, and its kinetic energy becomes four times as large. Why four times, rather than two?
A subway car slows to half its speed, mass unchanged. What happens to its kinetic energy?