The 2013 Tesla Model S received a top safety rating by the National Highway Safety Administration. Top scores.

So, what makes this car safer than other cars? There are several tests, but let's look at the frontal crash. In this test (seen above in the video), the car is smashed into a stationary barrier with a starting speed of 35 mph. For this collision, a safer car gives the passenger a lower acceleration. That's the goal of a safe car.

## Crash Course on Acceleration

These crashes are just happening in one dimension. That means that I can just look at the horizontal acceleration and treat it as a scalar (instead of writing them as vectors). With this in mind, I can define the acceleration of a passenger in the car as:

In this test, all cars will start with the same speed of 35 mph (15.6 m/s) and most will have a final speed of 0 m/s. Yes, some cars might "bounce" back and have a final negative component of velocity. That would increase the acceleration. For now, let's just assume that all the cars have the same final speed of 0 m/s. In that case, you can see that the only thing that could be different is the time of the collision. A longer collision time will give a smaller acceleration.

Sometimes it's better to think about the acceleration in terms of the stopping distance instead of the time. You can see in the video above that the driver in the car keeps moving forward during the collision with the wall. The greater the collision distance, the smaller the acceleration.

How do we remove the time part of the equation above? Start with the definition of the average acceleration during this time interval.

Now I can use another definition of the average velocity: