Applying Physics with Old/New School Investigative Techniques To Find The Truth

#### Where the Math Came From

Much of the work of accident analysis and reconstruction involves the application of general physical laws to the particular situation at hand.

These physical laws are expressed in terms of Newtonian mechanics, which was developed by the great English scientist Sir Isaac Newton in the seventeenth century. Newtonian mechanics is the base science of physics and engineering. Today the development and application of basic Newtonian mechanics is almost exclusively the province of engineers in that physicists, for the most part, conduct basic research only in "new physics" areas such as quantum mechanics, relativistic physics, etc. ## The 3 Laws of Motion

#### Newton wrote three laws of motion which relate kinematic phenomena to something else; forces.

1. First Law – Law of Inertia:  A body at rest remains at rest, a body in motion remains in motion at a constant speed along a straight line unless acted upon by an outside force. (Energy of motion or Kinetic Energy)

2. Second Law – Law of Acceleration:  The net resultant force applied to the body is equal to the first time-derivative of the momentum function. Or roughly: if acted upon by an outside force, the center mass of the body will accelerate in the direction of the force.  The acceleration of the center of mass is directly proportional to the force acting upon it and inversely proportional to its mass.
Force = Mass x Acceleration.

3. Third Law – Law of Impulse:  For every action there is an equal and opposite reaction.  These opposing forces are equal in magnitude and opposite in direction. You push on the wall- the wall pushes back. The pusher and the pushed, the striker and the struck both experience forces of the same magnitude but of opposite direction. ## KINEMATICS: THE ANALYSIS OF MOTION

#### More Science from Newton

Velocity

Velocity is the rate of change of the position of a body over time (velocity = distance/time). Velocity is a vector, which means it has both a magnitude and direction. Thus, 30 miles per hour north, or 20 meters per second along the X axis, are both velocities. Note that the more common term, Speed, is a velocity without a direction, so that 30 miles per hour or 20 meters per second are speeds, and not velocities, since no direction is specified.

Acceleration:

Acceleration is the rate of change in velocity (acceleration = velocity/time). Thus, any time a body changes its rate of travel or its direction of travel, it is said to be accelerating. Acceleration is a vector requiring both magnitude and direction. Thus, for example, 32.2 ft/sec/sec., downward toward the center of the earth, is the acceleration vector of all bodies on the surface of the earth. If the support collapses, for example, if a person falls off a ladder, they will increase their velocity at a rate of 32.2 ft/sec/sec. At the end of one second of free fall, they will be traveling at a rate of 32.2 ft/sec. which is approximately 22 miles per hour. They will have fallen approximately 16.1 feet in this one-second interval. (D = 1/2 a t x t = 1/2 x 32.2 x 1 x 1 = 16.1). 