The Physics of Car Crashes—and Why You Should Avoid Them

Two cars in crash test
“It’s not the fall that kills you; it’s the sudden stop at the end.”
― Douglas Adams

That quip by famed satirist and author of the 5-book “trilogy” The Hitchhiker’s Guide to the Galaxy may be moderately funny (all right, somewhat lame), but it also happens to be literally true. The scientific basis underlying this assertion can be expressed as a two-part logical equation, where…

  • “Vi” is your initial velocity
  • “t” is the total length of time of your fall
  • “a” is acceleration due to gravity as you fall
  • “Vf” is final velocity

…and where…

  • “m” is momentum
  • “ΔV” is change in velocity
  • “ΔT” is the time it takes to stop falling
  • “F” is force

Equation for falling and stopping

The first half of the equation denotes the fall (which is not fatal); the second half denotes the sudden stop (which most assuredly will be). Put another way, it’s not gravity you have to worry about, but Force.

The nature of the mathematically derived Force involved in such a fall is almost identical to that of a car crash, except it occurs on a (more or less) horizontal plane rather than a vertical one. To witness this Force in action in an automobile scenario, one need only watch one of the numerous Crash Test Dummy videos available on YouTube.

To grasp how Force relates to the abstract physics of car crashes (and so better appreciate the pragmatic aspects of this concept), we can delve back in time to more than 300 years ago—long before the first automobile rolled off the assembly line—when mathematician and all-around genius Sir Isaac Newton published his epochal work, Mathematical Principles of Natural Philosophy. In that work he laid out the three laws of motion, all three of which have direct application to how we drive our cars and what happens when we crash them. Those laws can be summarized as follows:

  1. “A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force.” Also called the Law of Inertia, this simply means that things cannot start, stop, or change direction all by themselves. It takes some external force acting upon them to cause a change in either a resting or moving state.
  2. “The force acting on an object is equal to the mass of that object times its acceleration.” This law describes in mathematical terms what happens to an object when it is acted upon by an external force.
  3. “For every action, there is an equal and opposite reaction.” In other words, this is what happens when one object exerts a force against another object. Forces never occur alone but always in pairs: when one body pushes against another, the second body pushes back just as hard.

Finally, one other law of physics has application to car crashes, and that is the Law of Conservation of Energy, first proposed by Julius Robert Mayer in 1842. Also called the “First Law of Thermodynamics,” it states simply that energy is neither created nor destroyed. It can only be transformed or transferred.

What Happens in a Car Crash According to Physics

The potential energy contained in your car’s fuel source (whether it be gasoline or EVB) is converted to kinetic energy once you start the car, step on the pedal, and begin accelerating down the road. While your body may seem to be “at rest” relative to the car itself in which you are driving, in reality it is in motion at the same speed as the car. That is an illustration of Newton’s First Law of Motion.

According to the Second Law, the combined mass of you and your car as they accelerate together constitute an exponentially increasing Force. The faster you go, the greater the Force.

Stopping the car is an illustration of the Third Law (as well as the Law of the Conservation of Energy). Whether you stop the car by hitting the brakes or by hitting a tree, the principle is exactly the same. When you brake, you are exerting a Force on your momentum; the equal and opposite reaction to that manifests itself in several ways. It can be felt in the slight forward inertial push of your body against your seatbelt, and it also occurs at the same time in the friction wear-and-tear on the tires and in the heating of the brake pads. In other words, the energy of your momentum is transferred to you, your tires, and pads. In the case of hitting the tree, on the other hand, energy is transferred via the injury to the tree, the damage to the front of your car, and whatever bruises or broken bones you may sustain.

Looked at another way, braking is nothing more than a controlled crash; and crashing is nothing more than an instance of out-of-control braking. Either way, energy is conserved.

Of course, the above example is a much simplified view of the physics of car crashes. No two collisions are exactly the same. Side-swiping a vehicle is different from a head-on collision, which means the complicated physics involved are different. In addition, speed, the make and model of the vehicle(s) involved, the elasticity of the object hit, and other factors affect the nature and outcome of a crash. And in high-speed crashes, the inscrutable laws of Chaos Theory come into play, where minuscule factors are magnified far beyond their normal triviality.

Fortunately, cars manufactured nowadays are designed first and foremost with safety in mind. In the early days of automobile manufacturing, cars were essentially rigid containers on wheels lacking seatbelts, airbags, and other safety features. In an accident, virtually all the energy of the crash was transferred directly to the occupants of the vehicle, often with horrific results.

Today’s cars feature not just seatbelts and airbags, but also bumpers and crumple zones designed to absorb as much of the kinetic energy of the crash as possible, thus sparing frail human bone and flesh the worst effects of that deadly transfer of energy of a car in motion becoming a car at rest.

Always remember that it’s up to you, as the driver, to determine how safely “energy is conserved.” Braking is always better than crashing! Take control. That means: don’t speed, don’t tailgate, drive defensively, and be cognizant of potential hazards far ahead of you on the road (think of it as Einsteinian Quantum Time Travel for Drivers).

Yet accidents will happen, no matter what. If you are unlucky enough to be involved in one and your car’s body is damaged in some way, Keri Coach will be happy to repair it for you.

If you are interested, this video gives another good, brief overview of the physics of car crashes.