# Driving Towards a Wall, Should You Stop or Turn?

This is just a fun physics question. It goes like this:

Imagine that you are in a car on a flat road. Boom. All of a sudden, there is a wall in the road. Where did that even come from? Well, you don’t have time to contemplate the existence of a wall. You need to take an action. Should you press the brake and stop the car? Or should you steer and turn to avoid the wall?

Of course we are going to solve this problem, but we need to make some assumptions first.

- When a car both stops and turns, it’s due to an interaction between the tires and the road. Let’s say that this is the static friction force (no sliding) and that this force is the same for both turning and stopping.
- Both the wall and the road are infinitely wide. So, you would have to make a complete 90 degree turn to avoid the wall.

Now for the physics.

# Stopping

I have a car of mass m moving with a velocity v moving towards a wall.

If we use the normal model for the static friction force, then the following would be true.

Of course the static friction force is a force of constraint — it has whatever value is needed to prevent the two surfaces from sliding with respect to each other. However, there is a maximum limit to the static friction force (that’s why there’s the less than or equal to sign). Since we want the car to stop in the shortest distance, we need the maximum friction. We can just use a normal equal sign here.

What about the normal force? If the car is on flat ground then the acceleration in the vertical direction would be zero m/s². The net force in the vertical direction must also be zero. There would only be two forces in the vertical direction, the normal force (pushing up) and the downward gravitational force (m*g where g is the gravitational field with a value of 9.8 Newtons per kilogram). So, N = mg. Nice.

Putting this together, we get a maximum static friction force of: