On Speed

“If everything is under control, you’re going too slow.”

– Mario Andretti

When Two Cars Hit Each Other

Consider this horrible scenario:

“Two cars crashing head on at 50 mph is the same as one car crashing into a wall at 100 mph.”

Of course, a head on collision is no picknick, but fortunately, the scenario is not true. Consider Newton’s 3rd Law: ‘Every reaction has an equal and opposite reaction.’

This explains that although the two-car crash doubles the speed, the energy of the crash is transferred to twice the mass resulting in a crash that looks like just one car hitting a wall at 50 mph.

Therefore, 10 + 10 is not the same as 40.

So, why are two cars crashing into each other not the same as one car going into a wall at twice the speed?

In terms of energy, the energy of motion is called kinetic energy. Kinetic energy depends on the square of the velocity. This means a car moving at twice the speed will have 4 times the kinetic energy.

Consider the following points:

• Forces are an interaction between two objects. Car 1 pushes on Car 2 in the same way as Car 2 pushes on Car 1, this is an equal interaction.
• A force on an object changes the object’s momentum (where momentum is mass times velocity).

In the scenario, the force of the wall exerted on the car and the force of the car exerted on the wall have the same magnitude. Now, what if the wall is replaced with another identical car travelling at the same speed?

Since the initial momentums are the same and the forces are same, the effects are the same on the two cars. So, two cars are the same as one car into a wall. However, when the impact speed hitting the wall is doubled, the car will have a different initial momentum, therefore, the crash will not be the identical. Initially, it seems unlikely, but it’s true.

“Our only kiss was like an accident – a beautiful gasoline rainbow.”
– Alice Sebold, The Lovely Bones