Does doubling speed double kinetic energy?
Short answer: KE = ½mv², so it scales with v². Double v gives 4 times KE (and about 4 times braking distance).
The trap
The wrong idea
“Doubling speed doubles kinetic energy.”
It sounds reasonable, and a lot of JEE/NEET aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
A car's speed goes from 20 to 40 km/h. Its kinetic energy becomes:
- 2 times
- 4 times
- 8 times
Show the answer
B. 4 times
KE = ½mv², so it scales with v². Double v gives 4 times KE (and about 4 times braking distance).
The click
Kinetic energy is KE = ½mv². Because v is squared, kinetic energy grows with the square of speed. Double the speed and KE becomes 2² = 4 times as large; triple it and KE becomes 9 times as large.
From 20 km/h to 40 km/h: KE₂/KE₁ = (40/20)² = 4. The mass cancels, so this holds for any car. Units don't matter for a ratio, as long as both speeds are in the same unit.
Why it matters on the road: to stop, the brakes must remove all that kinetic energy by doing work, roughly F × d for a fixed maximum braking force F. So the braking distance d = KE/F also grows about four times when speed doubles. A car at 40 km/h needs roughly four times the braking distance it needs at 20 km/h, and the distance covered during the driver's reaction time, which grows only in proportion to speed, comes on top of that.
Contrast this with momentum, p = mv, which simply doubles when speed doubles. Mixing the two up is a common slip: momentum is linear in v, kinetic energy is quadratic. Also, since KE = p²/2m, two objects with the same momentum have kinetic energies inversely proportional to their masses, so the lighter one carries more kinetic energy.
Got this one? The Knot Scan finds the misconception you don't know you have, in 8 questions.