Question

when traveling twice as fast your kinetic energy is increased ______. view available hint(s)
○ by two times
○ by three times
○ by four times
○ not at all
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Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy (KE) is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Step2: Calculate KE for Original Velocity

Let the original velocity be $v_1 = v$ and mass be $m$ (mass is constant). So original KE, $KE_1 = \frac{1}{2}mv^2$.

Step3: Calculate KE for Doubled Velocity

When velocity is doubled, $v_2 = 2v$. New KE, $KE_2 = \frac{1}{2}m(2v)^2 = \frac{1}{2}m\times4v^2 = 4\times(\frac{1}{2}mv^2)$.

Step4: Find the Factor of Increase

Since $KE_1 = \frac{1}{2}mv^2$, then $KE_2 = 4KE_1$. So the kinetic energy increases by four times.

Answer:

by four times (corresponding to the option "by four times")