If one vehicle is going 20 mph and another is going 60 mph, how many times greater is the force at impact of the 60 mph vehicle compared to the 20 mph vehicle?

In understanding the relationship between speed and the force of impact, it is crucial to grasp the principle of kinetic energy. The kinetic energy of a vehicle is calculated using the formula:

[ KE = \frac{1}{2} mv^2 ]

Where ( m ) is the mass of the vehicle and ( v ) is its velocity.

When considering two vehicles with different speeds, we see that the kinetic energy is proportional to the square of their speeds. For the 20 mph vehicle, its kinetic energy is proportional to ( (20)^2 ), which equals 400. For the 60 mph vehicle, the kinetic energy is proportional to ( (60)^2 ), yielding 3600.

To compare the impact forces, we take the ratio of their kinetic energies:

[ \text{Ratio} = \frac{KE_{60 mph}}{KE_{20 mph}} = \frac{3600}{400} = 9 ]

This calculation reveals that the force at impact of the vehicle traveling at 60 mph is nine times greater than that of the vehicle traveling at 20 mph. Understanding this concept underscores the significantly increased dangers associated with higher speeds in collision scenarios, highlighting the importance of speed management on the