When the speed of a car is halved, its kinetic energy is

Analyze the question: The speed of a car is cut to half. We need to know what happens to its kinetic energy.

Concept: Kinetic energy depends on mass and the square of speed:

KE = ½mv²

Because KE ∝ v², any change in speed affects KE by the square of that change.

Step-by-step solution:

1. Initial kinetic energy: KE₁ = ½mv²
2. New speed: v₂ = v/2
3. New kinetic energy: KE₂ = ½m(v/2)² = ½m(v²/4) = ¼(½mv²) = ¼ KE₁

So the kinetic energy becomes one quarter of its original value, which means it is quartered.

Check against the options:

• A. Doubled: incorrect
• B. Quartered: correct
• C. Halved: incorrect (this would happen only if KE were directly proportional to v)
• D. Quadrupled: incorrect (this would happen if the speed were doubled)

Exam tip: Remember "square the change." If speed is multiplied by a factor k, KE is multiplied by k².

• Speed × 2 → KE × 4
• Speed × ½ → KE × ¼
• Speed × 3 → KE × 9

The same idea applies to many JAMB and WASSCE questions on kinetic energy and stopping distance.