Question

1. if you are able to reduce your speed by half before crashing into a concrete post, the kinetic energy experienced in the crash will be reduced by four times.

a. true
b. false

Explanation:

Kinetic energy is given by the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity (speed, in this context). If speed \( v \) is reduced by half, the new speed \( v'=\frac{v}{2} \). The new kinetic energy \( KE'=\frac{1}{2}m(v')^2=\frac{1}{2}m(\frac{v}{2})^2=\frac{1}{2}m\frac{v^2}{4}=\frac{1}{4}(\frac{1}{2}mv^2)=\frac{KE}{4} \). So the kinetic energy (and thus the energy experienced in the crash, related to impact) is reduced to a quarter of the original, which means it is reduced by four times (since original - new = \( KE-\frac{KE}{4}=\frac{3KE}{4} \)? Wait, no—"reduced by four times" here means the magnitude of the energy (the impact) is a quarter, so the reduction factor is such that the energy is 1/4, so the statement is True? Wait, wait, let's re-express: If original KE is \( KE \), new KE is \( KE/4 \). So the energy experienced in the crash (which is related to the kinetic energy, as the crash involves dissipating that energy) is reduced to 1/4, which is a reduction by a factor of 4 (since \( KE - KE/4 = 3KE/4 \) is the reduction amount? No, the question says "the kinetic energy experienced in the crash will be reduced by four times". Wait, maybe the wording is "reduced to a quarter" which is a reduction by a factor of 4 (since 1/4 of original is a 4 - fold reduction in magnitude). So the statement is True.

Answer:

a. True