For decades, a remarkable story of human ingenuity has been unfolding on our roads. Cars have become safer than ever before, equipped with seatbelts, airbags, and intelligent braking systems. As a result, the number of fatalities per mile driven has plummeted. Yet, a puzzling and disturbing counter-narrative has emerged: the total number of collisions and injuries is actually on the rise. We have engineered safer cars, but we have not engineered safer roads. This paradox is the central phenomenon of our new unit. To unravel it, we must shift our perspective from the slow, geologic time of tectonics to the split-second timescale of a collision, where the laws of motion write their consequences with brutal clarity.

Our investigation begins not with physics equations, but with a surprising pattern in public health data. If cars are safer, why are more crashes happening? What factors could be contributing to this trend? Could it be the design of our roads, changes in driver behavior, or the sheer number of vehicles? Posing these questions transforms a simple statistic into a compelling scientific puzzle. The first step for any scientist or engineer is to analyze the available data to understand the scope of the problem.

To understand the physics of a collision, we must first learn the language used to describe motion itself, a field known as kinematics. The key terms are velocity (how fast an object is moving and in what direction) and acceleration (the rate at which an object’s velocity changes). A car traveling at a steady 60 miles per hour has a constant velocity. A car braking for a stoplight is accelerating—in this case, its velocity is decreasing. A driver’s ability to control their vehicle’s velocity and acceleration is fundamental to safety.

Imagine trying to stop two different objects moving at the same speed: a bowling ball and a tennis ball. The bowling ball is much harder to stop. This intuitive idea—that some moving objects have more ‘unstoppability’ than others—is captured by the physics concept of momentum. Momentum is defined as an object’s mass multiplied by its velocity ($p = mv$). A massive truck moving slowly can have the same momentum as a fast-moving car. In any collision, it is the momentum of the vehicles that must be dealt with. The entire goal of safety engineering is to manage the change in momentum in a way that is survivable for the occupants.

How do you change an object’s momentum? You apply a force. But the duration of that force matters just as much as its strength. Think about catching a fast-moving baseball. You instinctively pull your hand back as you catch it, extending the time of impact. This reduces the sting. This relationship between force and time is called impulse. Impulse is the force applied to an object multiplied by the time interval over which it is applied ($J = FΔt$). Critically, the impulse applied to an object is exactly equal to the change in its momentum ($FΔt = Δp$). This is the impulse-momentum theorem, and it is the single most important concept in the design of vehicle safety systems. To reduce the force on an occupant, engineers must find ways to increase the time over which their momentum changes.