Kinematics

Symbols in Formulas

• "v" represents velocity
• "t" represents time
• "a" represents acceleration
• "d" represents distance

SUVAT

• SUVAT describes variables in motion equations
• "s" stands for displacement/distance
• "t" stands for time
• "a" stands for acceleration
• "u" stands for initial velocity
• "v" stands for final velocity

Initial Data

• Initial data refers to the information available at the start of a problem

Kinematics

• Kinematics is the study of motion occurrences
• Speed describes how fast an object is moving
• Meters per second (m/s) is the unit for speed
• Velocity is the speed of an object in a specific direction
• Meters per second (m/s) is the base unit for velocity
• Velocity is a vector quantity
• Curve velocity uses the shape of a curve to calculate area and distance
• Displacement describes the change in position and magnitude
• Displacement is a vector quantity
• Vectors have both direction and magnitude

Metric System

• The metric system is a base unit system
• Base units include meters (m), grams (g), liters, and seconds
• Newtons (N) are not a fundamental unit
• Meters, grams, liters, and seconds are fundamental units
• Metric system describes length changes in space
• giga(G), mega(M), kilo(k), hecto(h), deca(d), base/mid, deci(d), centi(c), milli(m), micro, nano(n) are length measurements
• Each unit in the metric system represents a type of meter
• k= km, c=cm, m=mm
• To convert measurements: 24000 cm = 0.00024 Mm

Parallax

• Parallax refers to the shift in an object's position when the viewing angle changes

Physics and Math

• Physics is related to math via equations

Linear Relationships

• Physics graphs can show linear relationships, forming a straight line
• In a direct relationship, the line passes through the x and y-axis origin (zero)
• Direct relationships can be expressed as y = mx + b
• "m" represents the slope
• "y" represents the dependent variable

Slope Calculation

• Slope is calculated by rise/run

Uniform Speed

• speed = displacement/time, or v = s/t

Inverse Relationships

• Inverse relationships are expressed by the equation xy=k or y=k/x
• Variable changes are possible in an equation
• The line won’t touch any point in the graph
• Graphs of inverse relationships results in a curve

Triangle Symbol

• A triangle appearing behind a symbol indicates change of that symbol
• Change of time and Change of speed

Quadratic Equations

• Represented as y=kx^2
• The graph starts from a point and curves after leaving the point

Describing Motion

• Motion can be described using graphs, data tables, equations, and conclusion sentences

Conversions

• 1000 meters equals 1 kilometer
• 100 centimeters equals 1 meter
• 100,000 centimeters equals 1 kilometer

Metric Conversions

• Divide by 1000, 100, or 100000 when converting to a higher metric
• Multiply by 1000, 100, or 100000 when converting to a lower metric

Scalars

• Scalars are numbers that only have magnitude

Vectors

• Vectors are numbers that have both magnitude and direction
• Vectors have direction
• Vector symbols are the same as scalar symbols, but with an arrow above

Relative Motion

• Relative motion describes one object's motion in relation to another
• The formula accounts for direction:
• velocity of object A relative to object B = velocity of object A - velocity B
• Velocity of object B relative to object A= VB-VA
• If objects A and B move in the same way, add their velocities together
• Pythagorean theorem is used if the route of something is in 2D and is north-east, north- west, or same for south

Average Velocity

• Average velocity is calculated by change in distance / change in time
• The simplified version of average velocity is Vave
• When constant, average velocity results in data with a constant velocity

Slope Sign

• A positive slope indicates an upward direction on the graph
• A negative slope indicates a downward direction
• A zero slope indicates no change or no motion

Position-Time Graphs

• Position-time graphs display speed, relationship between distance and time
• Data from position-time graphs can calculate the average velocity
• Lines can be linear or curved
• d-t graphs are simplified
• The slope indicates object velocity
• Displayed as a table

Velocity-Time Graphs

• Velocity-time graphs show the relationship between speed and time

Slope of Velocity-Time Graphs

• The slope equals acceleration
• Slope = acceleration, described by
• Acceleration can be described where change of time = final time - initial time
• V final = final velocity
• v initial= the first velocity

Area of Velocity-Time Graphs

• Area of v-t graph equals distance
• Calculated by d= change in time (vf+vi)/2
• change in time= time final - time initial
• Change in velocity= velocity final- velocity initial

Acceleration and Distance formulas

• d= velocity initial times change in time +(acceleration times ( change in time)^2)/2
• Velocity initial= original velocity
• Change in time= time final - time initial
• acceleration = (change in velocity)/ change of time
• 2ad = (v final)^2 - (V initial)^2 when finding the time and acceleration
• a= acceleration = change in velocity/ change in time
• Velocity inintial distance= (velocity final times change of time)- (a(change of time)^2)/2
• a = acceleration= change of velocity/ change of time
• Final velocity = at+ vi

Acceleration Defined

• Acceleration is the change of velocity (speed and location)
• Calculated by a= change in velocity / time

Free Falling Objects

• Gravity causes acceleration
• Near earth, gravity equals 9.81 m/s^2
• Constant free fall acceleration, g, results from gravity

Tossed Motion

• Tossed Motion is Not equal to zero
• The time of going up equals the time going down
• Deceleration is equal to -9.81m/s^2, with a final velocity of 0
• Acceleration is equal to 9.81, with a initial velocity of 0
• If an object flys above gravity, the energy equals -9.81 m/s^2 and will decelerate

Horizontal Projectile Motion

• Two the projectiles will strike the ground from an object that move horizontally
• Occurs when an object is dropped and hits at the same time
• Same gravity, therefore same time is received
• Object speed is constant unless acted upon by an external force
• Gravity formula
• Total time of a projectile in the air: T= (2u sin θ)/g
• g is equal to gravity
• theta is the angle
• Horizontal distance of a projectile: R = (u^2 sin 2 θ)/g
• Maximum height of a projectile: h = (u^2 sin^2 θ)/ 2g
• Formula for horizontal or vertical position:
• x= vtcos θ
• y= y+vtsinθ-(gt^2)/2
• velocity
• vx=vcosθ
• vy=vsinθ-gt
• Acceleration is change of speed and its position/magnitude
• a=change in velocity/time taken

Dynamics

• Dynamics the study of why motion occurs

Newton’s Laws of Motion

• Issac Newton studied interactions between forces and objects
• Four major types of forces: gravitational, electromagnetic, strong nuclear, weak nuclear
• Gravitational forces are the weakest, and observable
• Gravity is equal to a = 9.81 and is found to be a falling force
• Electromagnetic forces include magnets
• Strong nuclear forces hold particles together in the nucleus
• Weak nuclear forces happens in Natural decay of an nucleus in an atom
• Weaker force that particle escapes
• Force is energy and is described as a push or pull
• Force has both magnitude and direction
• Inertia is the nature of objects to resist changes in their state of motion
• An object remains at rest will remain so unless acted upon by an external force
• Inertia increases with mass
• Higher mass is correlated to higher inertia

Laws of Motion

• First law states all objects remain at rest or with constant speed of the force is balance
• The force accelerate the force is unbalance
• Force is determined by F=ma
• F equals mass times acceleration
• F is net force. It is calculated in newtons
• Mass is how heavy an object is, measured by kg
• a= acceleration of the object
• Acceleration is proportional to net force
• Third law or Action-reaction law means equal and opposite reaction to every action force
• It creates force that will bounce back
• Scalars are physical quantities described by magnitude
• Vectors are physical quantities described by both magnitude and direction
• Vectors includes a position arrow
• One dimension is excluded
• One dimension is excluded
• Assume directions is when the question assume it
• Scalar quantities add arithmetically
• Vectors may be used at angles

Vector Problems

• Pythagorean theorem and trigonometry is required to find the total distance
• Cosine and sine law is used for nonright triangle
• When a boat is moving, the time of going from the base to different parts of the boat is the same, except for some
• Objects can be launched at an angle with accelerated or constant motion
• Angles can be launched by gravity or horizontal movement
• Trig is vital for upward angles
• Mass is constant and based on kg Weight is based on gravity and is changeable Weight formula = Fg=ma
• Fg is weight, a is acceleration
• Calculate the Pythagorean theorem if the force is veritcal
• Weight can change due to the gravity in Apparent losses and gains in weight.
• weight increases in when accelerating an object

Free Body Diagram

• Four main forces are in a free body diagram

Forces

• Fg-force of gravity is the force pushing down objects. It’ the x axis when the object is in projectile motion
• Fn- normal force is the force is pushing against gravity
• Ff-force of friction is a force decelerate the object
• Is a force to move when the object is going down
• Gravity create friction
• Fapp- applied force describes any push or pilling done to an object

Horizontal Surfaces

• The diagram shows an object horizontally.
• For the Fapp is at the front and the friction force pulling when It moves at a downward angle
• The forces are equal to when no movement occurs
• Friction occurs in 2 steps being static and kinetic
• Static friction is force required to prevent is still or moving
• friction increases depending on coefficient
• friction decreases when the coefficient is reduced
• dynamic friction is lower than static friction
• net force Fnet= Force applied force ( extra force) - friction