What happens to kinetic energy if the speed of an object doubles?

What happens to kinetic energy if the speed of an object doubles?

• A. Kinetic energy doubles
• B. Kinetic energy quadruples
• C. Kinetic energy remains the same
• D. Kinetic energy is halved

Answer: (B)

Kinetic energy is defined by the equation \( KE = \frac{1}{2} mv^2 \), where \( m \) represents the mass of the object and \( v \) is its velocity. When assessing the effect of doubling the speed of the object, we can substitute \( 2v \) for \( v \) in the kinetic energy equation. Substituting gives us: \[ KE' = \frac{1}{2} m (2v)^2 = \frac{1}{2} m (4v^2) = 2mv^2 \] This shows that the new kinetic energy \( KE' \) is four times the original kinetic energy \( KE \). Therefore, when the speed of the object doubles, the kinetic energy quadruples. This understanding is crucial in mechanics, as it highlights the nonlinear relationship between speed and kinetic energy.

Kinetic energy is defined by the equation ( KE = \frac{1}{2} mv^2 ), where ( m ) represents the mass of the object and ( v ) is its velocity. When assessing the effect of doubling the speed of the object, we can substitute ( 2v ) for ( v ) in the kinetic energy equation.

Substituting gives us:

[

KE' = \frac{1}{2} m (2v)^2 = \frac{1}{2} m (4v^2) = 2mv^2

]

This shows that the new kinetic energy ( KE' ) is four times the original kinetic energy ( KE ). Therefore, when the speed of the object doubles, the kinetic energy quadruples. This understanding is crucial in mechanics, as it highlights the nonlinear relationship between speed and kinetic energy.