Question

class e general knowledge question #17 / 50
you must not drive at excessive speeds. if you double the speed of a car, the force of impact in a crash is
select a letter to choose your answer.
a doubled.
b four times as great.
c five times as great.

Explanation:

Step1: Use the kinetic energy formula

The kinetic energy formula is \(K = \frac{1}{2}mv^{2}\), where \(m\) is the mass of the car (assumed constant) and \(v\) is the speed.

Step2: Analyze the effect of doubling the speed

Let the initial speed be \(v_1 = v\), then the initial kinetic energy \(K_1=\frac{1}{2}mv^{2}\). When the speed is doubled, \(v_2 = 2v\), and the new kinetic energy \(K_2=\frac{1}{2}m(2v)^{2}=\frac{1}{2}m\times4v^{2} = 4\times\frac{1}{2}mv^{2}\). So \(K_2 = 4K_1\). The force of impact is related to the kinetic - energy (more kinetic energy means more work done during the crash, which is related to a greater force of impact over the deformation distance).

Answer:

B. Four times as great.