Question

1. which of the following regarding a collision is/are true?

a. if you triple your speed your force of impact will be three times greater
b. speed has little effect on impact forces
c. if you double your speed, the energy dissipated in a crash is four times greater
d. if you double your speed, the energy dissipated in a crash is two times greater

Explanation:

To determine the correct answer, we analyze each option using the physics concept of kinetic energy (\(KE = \frac{1}{2}mv^2\)) and impact force (related to change in momentum, \(F\Delta t=\Delta p\), and kinetic energy for energy dissipation in a crash).

• Option a: Impact force depends on momentum change (\(\Delta p = m\Delta v\)) and time of impact. If speed triples, \(\Delta v\) (for a crash, assuming stopping from speed \(v\) to 0, \(\Delta v = v\)) triples, so momentum change triples. But impact force also depends on impact time (\(F=\frac{\Delta p}{\Delta t}\)). If impact time changes (e.g., due to crumple zones), the relationship isn’t simply "three times greater" without controlling time. So a is incorrect.
• Option b: Speed has a significant effect on impact forces (via momentum) and energy (via \(v^2\) in KE). So b is incorrect.
• Option c: Kinetic energy is proportional to \(v^2\) (\(KE = \frac{1}{2}mv^2\)). If speed \(v\) doubles to \(2v\), new KE is \(\frac{1}{2}m(2v)^2 = 4\times\frac{1}{2}mv^2\) (four times the original KE). In a crash, the energy dissipated equals the initial KE (assuming all KE is dissipated). So doubling speed makes energy dissipation four times greater.
• Option d: As shown for c, energy is proportional to \(v^2\), so doubling speed quadruples energy, not doubles it. So d is incorrect.

Answer:

c. If you double your speed, the energy dissipated in a crash is four times greater