The momentum of an object, which is the product of its mass and velocity, is directly related to its stopping distance; a larger momentum requires a larger force or more time to bring the object to a stop, hence a longer stopping distance.
The momentum of an object is directly proportional to its mass and its velocity, as defined by the formula p = m × v, where p is momentum, m is mass, and v is velocity. When an object is moving, its stopping distance depends on the momentum it has; a larger momentum will generally require a longer stopping distance due to the need to change this momentum to zero, which can be achieved by applying a force over a period of time, known as an impulse. Stopping distance increases significantly with speed due to the square relationship between velocity and kinetic energy (K = p²/2m).
In summary, an object with greater mass or higher velocity (larger momentum) necessitates a larger force or more time to reduce its momentum to zero, resulting in a longer stopping distance. This is critical in real-world scenarios, such as implementing reduced speed zones near schools where stopping quickly is essential for safety.