Question

which statement best describes the relationship between speed and kinetic energy? a. when the speed of an object doubles, its kinetic energy doubles. b. when the speed of an object doubles, its kinetic energy quadruples. c. when the speed of an object doubles, its kinetic energy stays the same. d. when the speed of an object doubles, its kinetic energy is reduced by half.

Explanation:

Step1: Recall the formula for kinetic energy

The formula for kinetic energy is \(K.E.=\frac{1}{2}mv^{2}\), where \(m\) is the mass of the object and \(v\) is its speed.

Step2: Analyze the effect of doubling the speed

Let the initial speed be \(v_{1} = v\), so the initial kinetic energy \(K.E._{1}=\frac{1}{2}mv^{2}\).
If the speed doubles, \(v_{2}=2v\). Then the new kinetic energy \(K.E._{2}=\frac{1}{2}m(2v)^{2}=\frac{1}{2}m\times4v^{2} = 4\times(\frac{1}{2}mv^{2})\).
Since \(K.E._{1}=\frac{1}{2}mv^{2}\), we have \(K.E._{2} = 4K.E._{1}\).

Answer:

B. When the speed of an object doubles, its kinetic energy quadruples.