1.4 Momentum and Newton's 2nd Law

In other words, if there's an «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»n«/mi»«mi»e«/mi»«mi»t«/mi»«/mrow»«/msub»«/math», there's a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8710;«/mo»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«/math»  which shows there is a relationship between Newton's second law and momentum.

A moving vehicle has a momentum defined by the product of its mass and velocity. Changing either of these two quantities will cause a corresponding change in the momentum.  Both the mass and average velocity of modern vehicles is much larger than those of the past. This means that the amount of momentum on today's busy freeways is increasing. And according to Newton's second law, a large net force is required to make a large change in momentum quickly. In effect, this means that the modern car crash that involves a larger vehicle and/or one traveling at a high velocity will generate larger net forces because the time of the collision hasn't changed.

Can you think of what implications this has for both vehicle design and safety? Larger vehicles and/or those that travel at a high rate of speed require larger engines and brake systems and stronger steering systems.  All of these design features are required to change large amounts of momentum in short periods of time.

Newton's second law shows that the external, non-zero, net force acting on an object will be equal to the rate of change of the momentum of that object with respect to time.  

For example, to change the momentum of a large mass in a short time, such as a passenger car (even if it is moving at low velocity), a very large net force is required. The same is true for a smaller mass, such as a motorcycle if it travels at high velocity. In this form of Newton's second law, the mass, the time interval, and the velocity of the object (momentum) are considered.