Question

1. which change would increase the kinetic energy of a moving object the most? a. reducing the mass by half b. reducing the speed by half c. doubling the mass of the object d. doubling the speed of the object

Explanation:

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

• For option A: If mass is reduced by half ($m'=\frac{m}{2}$), new KE is $KE_A=\frac{1}{2}(\frac{m}{2})v^2=\frac{1}{4}mv^2$, which is a decrease.
• For option B: If speed is reduced by half ($v'=\frac{v}{2}$), new KE is $KE_B=\frac{1}{2}m(\frac{v}{2})^2=\frac{1}{8}mv^2$, a decrease.
• For option C: If mass is doubled ($m' = 2m$), new KE is $KE_C=\frac{1}{2}(2m)v^2=mv^2$, which is double the original ($KE=\frac{1}{2}mv^2$).
• For option D: If speed is doubled ($v' = 2v$), new KE is $KE_D=\frac{1}{2}m(2v)^2=\frac{1}{2}m\times4v^2 = 2mv^2$, which is four times the original.

Since doubling speed increases KE more than doubling mass, option D is correct.

Answer:

D. doubling the speed of the object