Mastering Physics Solutions Chapter 2 One-Dimensional Kinematics. You and your dog go for a walk to a nearby park On the way

and so on When you arrive at the park, do you and your dog have the same displacement? Have you traveled the same distance? Explain.. while the distance traveled by the dog is greate than the distance traveled by us

The distance is defined as a scalar quantity which is equal to how much ground that an object covered during its overall motion. The displacement is a vector quantity which is defined as how far an object travelled from its initial position

– Describe the effects of gravity on objects in motion.. – Describe the motion of objects that are in free fall.

Falling objects form an interesting class of motion problems. For example, we can estimate the depth of a vertical mine shaft by dropping a rock into it and listening for the rock to hit the bottom

The most remarkable and unexpected fact about falling objects is that, if air resistance and friction are negligible, then in a given location all objects fall toward the center of Earth with the same constant acceleration, independent of their mass. This experimentally determined fact is unexpected, because we are so accustomed to the effects of air resistance and friction that we expect light objects to fall slower than heavy ones.

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.[2]: 1.1 It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).. Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck’s solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein’s 1905 paper, which explained the photoelectric effect

The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle’s energy, momentum, and other physical properties may yield.

See Sections 1.1, 25.1-25.2 of your textbook for more information on these methods.. A differential equation is one which expresses the change in one quantity in terms of others

Sometimes, when you’re lucky, the physical situation has an analytic solution. For example, consider the relationship between velocity and time, for the case of constant acceleration:

That’s always the best way to go, since you can figure out the quantities of interest (position, velocity) for any time, with absolutely no error.. Unfortunately, in many situations, the physical relationships between quantities is more complicated, such as

This introduction to special relativity is for anyone who is already comfortable with the Newtonian concepts of velocity, acceleration, momentum, and energy. It is intended as a compromise between the extremely rushed treatments of relativity that appear in standard introductory physics textbooks, and the more leisurely treatments that appear in books dedicated to teaching just relativity

In my own introductory physics course I deliver these five lessons during five 50-minute class sessions, and we spend two more class sessions discussing the assigned homework problems. This is nearly double the class time for relativity that a traditional introductory course would allocate, but in my mind it’s the absolute minimum.

“Relativity” is short for what Albert Einstein called his “special theory of relativity”, published in 1905. This “theory” is a revised framework for the laws of mechanics