Driving Towards a Wall, Should You Stop or Turn?

Photo: Rhett Allain. Dogs shouldn’t drive, but would they turn or stop to avoid a wall?

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.