If velocity doubles for a body of fixed mass, kinetic energy changes by what factor?

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Multiple Choice

If velocity doubles for a body of fixed mass, kinetic energy changes by what factor?

Explanation:
Kinetic energy depends on the square of the speed, KE = 1/2 m v^2. If the velocity becomes 2v with the mass fixed, the energy becomes 1/2 m (2v)^2 = 1/2 m · 4v^2 = 4 × (1/2 m v^2). So the kinetic energy increases by a factor of four. This reflects that energy scales with velocity squared, so doubling speed requires four times as much energy (for the same mass).

Kinetic energy depends on the square of the speed, KE = 1/2 m v^2. If the velocity becomes 2v with the mass fixed, the energy becomes 1/2 m (2v)^2 = 1/2 m · 4v^2 = 4 × (1/2 m v^2). So the kinetic energy increases by a factor of four. This reflects that energy scales with velocity squared, so doubling speed requires four times as much energy (for the same mass).

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