How is kinetic energy affected if the velocity of an object is doubled?

• A. It quadruples
• B. It doubles
• C. It remains the same
• D. It halves

Answer: (A)

Kinetic energy depends on velocity squared, so changing speed has a squared effect. The formula is KE = 1/2 m v^2. If the velocity doubles, use v → 2v: KE becomes 1/2 m (2v)^2 = 1/2 m · 4v^2 = 4 × (1/2 m v^2). Therefore, kinetic energy quadruples when speed is doubled. This assumes the mass stays the same. If speed changes by a different factor, energy changes by the square of that factor (e.g., tripling speed gives nine times the energy).