# You’re Racing Toward a Wall. Should You Brake Hard—or Swerve?

I know it was a long time ago, but there was this interesting discussion about stopping a car on an episode of Car Talk. Should you just brake as hard as possible or should you brake and weave back and forth? The idea is that by weaving back and forth you increase your total distance traveled, but you might be able to stop in a shorter distance along the road (assuming it’s straight).

Actually, this is related to a fun physics question. Suppose you are driving along and headed towards a wall. Should you slam on the brakes or turn? Let’s assume that it’s an infinitely long wall such that you would have to turn a full 90 degrees in order to miss the wall. What should you do? Hurry, there’s no time. Actually, we do have time. Let’s calculate the required distance for these two cases.

### Stopping in a Straight Line

The easiest case is stopping in a straight line. If you have a car moving on a flat road, then there are essentially three forces acting on it during the stopping motion. Here is a force diagram.

The first force to consider is the gravitational force. This force pulls straight down and is equal to the product of the car’s mass (m) and the local gravitational field (g). The next force is called the normal force. It’s a force that is perpendicular to the ground and prevents the car from falling through the road. This force (labeled N) will be equal in magnitude to the gravitational force so that the total vertical force is zero.

Finally, there is the frictional force (Ff) between the tires and the road. This is a backwards-pushing force that decreases the car’s speed. Although friction is actually quite complicated, a simple model works in most cases. This model says that the maximum static friction (when two surfaces interact without relative motion) depends on the magnitude of the normal force. Here is the equation.