Chapter 2

Mechanics

It is the branch of physics formed by the combination of kinematics and dynamics.

Kinematics

It is the branch of mechanics that deals with the concepts that are needed to describe motion, without any reference to forces.

Dynamics

It is the branch of mechanics that deals with the effect that forces have on motion.

Displacement

It is a vector that points from an object's initial position to its final position, having a magnitude equal to the shortest distance between the two positions.

Displacement versus Distance

They are distinct physical quantities because displacement is a vector representing a straight line from start to finish, whereas distance is a scalar representing the actual length of the path traveled.

Average Speed

It is the distance traveled divided by the elapsed time required to cover the distance.

Average Velocity

It is a vector quantity defined as the displacement divided by the elapsed time.

Direction of Average Velocity

It is always the same as the direction of the displacement vector.

Instantaneous Velocity

It is the limit of the average velocity as the elapsed time interval becomes infinitesimally small.

Instantaneous Speed

It is the magnitude of the instantaneous velocity, representing the value indicated by an object's speedometer.

Average Acceleration

It is a vector quantity defined as the change in velocity divided by the elapsed time.

Direction of Average Acceleration

It is always the same as the direction of the change in velocity vector.

Instantaneous Acceleration

It is the limit of the average acceleration as the elapsed time interval becomes infinitesimally small.

Deceleration

It is a motion where the acceleration and velocity vectors point in opposite directions, causing the object's speed to decrease.

Speeding Up

It is a motion where the acceleration and velocity vectors point in the same direction, causing the object's speed to increase.

Kinematic Variables

They are the five physical quantities used to describe motion under constant acceleration: 1. displacement (x) 2. acceleration (a) 3. final velocity (v) 4. initial velocity (v0) 5. elapsed time (t).

Midway Average Velocity

It is the average velocity of an object under constant acceleration, calculated as one-half of the sum of the initial and final velocities.

First Equation of Kinematics

It is v = v0 + at, which relates final velocity, initial velocity, constant acceleration, and elapsed time, but does not contain displacement.

Second Equation of Kinematics

It is = 1/2 * (v0 + v) * t, which relates displacement, initial velocity, final velocity, and elapsed time, but does not contain acceleration.

Third Equation of Kinematics

It is x = v0 * t + 1/2 * a * t^2, where the first term represents the displacement if acceleration were zero, and the second term represents the additional displacement due to acceleration.

Fourth Equation of Kinematics

It is v^2 = v0^2 + 2ax, which relates final velocity, initial velocity, constant acceleration, and displacement, and is particularly useful when the elapsed time is unknown.

Deceleration versus Negative Acceleration

They are not synonymous because deceleration depends on the velocity and acceleration pointing in opposite directions, meaning deceleration can have a positive acceleration if the velocity is negative.

Multiple-Segment Motion

It is the problem-solving principle that when motion is divided into separate segments, the final velocity of one segment must be used as the initial velocity for the next segment.

Reasoning Strategy for Kinematics

They are the following steps:

1. Make a drawing to represent the situation

2. Decide which directions are positive (+) and negative (-) relative to a coordinate origin

3. Write down values with appropriate signs for the five kinematic variables

4. Verify that values for at least three variables are known and select the appropriate equation

5. For segmented motion, use the final velocity of one segment as the initial of the next

6. Keep in mind there may be two mathematically possible answers.

Free-Fall

It is an idealized vertical motion in which air resistance is neglected and the acceleration is constant, which is a highly accurate model if the distance of the fall is small compared to the Earth's radius.

Acceleration due to Gravity

It is the constant vertical acceleration experienced by all freely falling bodies at the same location, denoted by the symbol g, which points downward toward the center of the Earth.

Gravity

It is approximately 9.80 m/s² or 32.2 ft/s² near the Earth's surface, decreasing slightly with increasing altitude and varying slightly with latitude.

Free-Fall on the Moon

It is an environment where all objects fall with the same constant acceleration, but this acceleration is approximately one-sixth of the acceleration due to gravity on Earth.

Air Resistance

It is the force responsible for causing lighter objects like paper to fall slower than heavier ones; in its absence, all objects exhibit exactly the same acceleration.

Upward or Downward

This refers to the direction of the Free-Fall Motion under the influence of gravity alone, meaning a freely falling body does not necessarily have to be moving down.

Speed Symmetry

It is the characteristic where, at any given displacement above the point of release, the speed of a freely falling object on its upward trip is exactly equal to its speed on its downward trip.

Time Symmetry

It is the characteristic where the time required for a freely falling object to reach its maximum height is exactly equal to the time required for it to return to its initial release point.

Acceleration at Maximum Height

It is still equal to the constant acceleration due to gravity (g = 9.80 m/s² downward) even though the velocity of the object is momentarily zero.

Slope of a Position-versus-Time Graph

It is the graphical feature that represents the average velocity of the object if the graph is a straight line, and the slope of the tangent line represents the instantaneous velocity if the graph is a curve.

Slope of a Velocity-versus-Time Graph

It is the graphical feature that represents the average acceleration of the object if the graph is a straight line, and the slope of the tangent line represents the instantaneous acceleration if the graph is a curve.

Greek Letter Delta

This refers to the symbol (Δ) used in physics to signify a change in a variable, calculated as the final value minus the initial value.

Centimeter to Inch Conversion

It is the exact dimensional relationship where 1 inch is equal to 2.54 centimeters.

Average Value Notation

It is the practice of placing a horizontal bar above a symbol to represent the average value of a physical quantity.

ThrustSSC Record

It is the world land speed record of 341.1 m/s (763 mi/h) set in 1997 by a vehicle powered by two jet engines.

Velocity on a Circular Path

It refers to motion where speed is constant but velocity is constantly changing because the direction of travel changes continuously.

Independence of Velocity and Acceleration

It is the physical principle that an object's velocity and acceleration at any given instant are independent of each other.

Lunar Free-Fall Demonstration

It is the historical experiment performed by astronaut David Scott who dropped a hammer and a feather simultaneously on the moon to prove they fall with the same acceleration in a vacuum.

32.2 ft/s²

BE Value of Gravitational Acceleration, which is the standard value of acceleration due to gravity in the British Engineering system.

Mass Independence

It is the phenomenon where all objects falling near the Earth's surface in a vacuum accelerate at the exact same rate regardless of their mass.

Velocity-Time Relation under Constant Acceleration

It is the principle that when an object starts from rest with constant acceleration, its velocity doubles when the elapsed time doubles.

Displacement-Time Relation under Constant Acceleration

It is the principle that when an object starts from rest with constant acceleration, its displacement increases by a factor of four when the elapsed time doubles.