Safety regulations require that all cars traveling at a given speed be able to stop within a given distance. What must be the relationship between the minimum braking forces allowed by law for two cars whose masses have the ratio of 3 to 2?
Strategy We can use Newton's second law to relate the force to mass and acceleration. From your knowledge of kinematics, you know that the requirement for stopping in equal distances from the same initial speed for both cars means they must both have the same acceleration.
Solution We can write the two accelerations in terms of the braking forces F1 and F2 and the masses m1 and m2 as
When we set the accelerations equal we find
so
Discussion This result tells us that a larger braking force is needed to stop a larger (more massive) car in the same distance that a smaller (less massive) car is stopped.