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Steps to Draw a Motion Graph

Identify the type of graph, label axes with units, choose a scale, then plot points smoothly

Displacement vs Time Axes

Time on the x-axis, displacement on the y-axis

Velocity vs Time Axes

Time on the x-axis, velocity on the y-axis

Acceleration vs Time Axes

Time on the x-axis, acceleration on the y-axis

Straight Line on d-t Graph

Represents constant velocity

Curved Line on d-t Graph

Represents changing velocity (acceleration)

Flat Line on d-t Graph

Object is not moving

Positive Slope on d-t Graph

Object is moving in the positive direction

Negative Slope on d-t Graph

Object is moving in the negative direction

Steeper Slope Means

Greater velocity

Flat Line on v-t Graph

Constant velocity (no acceleration)

Slope of v-t Graph

Acceleration

Area Under v-t Graph

Displacement

Positive Area on v-t Graph

Object moves forward

Negative Area on v-t Graph

Object moves backward

Flat Line on a-t Graph

Constant acceleration

Positive Acceleration Graph

Velocity is increasing

Negative Acceleration Graph

Velocity is decreasing

Area Under a-t Graph

Change in velocity

Zero Acceleration on a-t Graph

Velocity remains constant

Changing Acceleration Graph

Acceleration is not constant

How to Tell If Object Is Speeding Up

Velocity and acceleration have the same sign

How to Tell If Object Is Slowing Down

Velocity and acceleration have opposite signs

Graphing with No Motion

Line is horizontal on displacement or velocity graphs

Graphing Constant Speed

Straight line on displacement graph or flat line on velocity graph

Units Matter on Graphs

Always include correct units on both axes

Smooth Curves vs Sharp Corners

Motion graphs should be smooth unless motion changes instantly

Displacement vs Time Graph

Tells you how an object’s position changes over time; the slope represents velocity

Velocity vs Time Graph

Tells you how velocity changes over time; the slope gives acceleration and the area under the graph gives displacement

Acceleration vs Time Graph

Tells you how acceleration changes over time; the area under the graph gives change in velocity

Acceleration

The rate at which velocity changes over time

Acceleration and Velocity in Circular Motion

In circular motion, acceleration is directed toward the center while velocity is tangent to the circle

Impulse

A force applied over a period of time that changes an object’s momentum

Momentum

The product of mass and velocity (p = mv)

Momentum Comparison

A truck at a stop sign has more momentum than a flying bug because momentum depends on mass and velocity

Impulse Definition

Impulse equals force times time (Impulse = FΔt)

Why We Have Air Bags

Air bags increase the time of collision, reducing the force on passengers

Types of Collisions

Elastic, Inelastic, and Perfectly Inelastic

Collision Equations

momentum before = momentum after (m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′)

Collision with KE Conserved

Elastic collisions conserve kinetic energy

Collision with Momentum Conserved

Momentum is conserved in all collisions

Newton’s First Law

An object at rest stays at rest and an object in motion stays in motion unless acted on by a net force

Newton’s Second Law

Force equals mass times acceleration (F = ma)

Newton’s Third Law

For every action, there is an equal and opposite reaction

Universal Law of Gravitation

All masses attract each other with a force proportional to their masses and inversely proportional to the square of the distance

Tripling Distance in Gravity

The gravitational force becomes 1/9 as strong

Doubling One Mass and Halving the Other

The gravitational force stays the same

Mass vs Weight

Mass is the amount of matter; weight is the force of gravity on that mass

Echolocation Animals

Bats and dolphins use echolocation

Fastest Medium for Sound

Sound travels fastest in solids

Speed of Sound in Air

Approximately 343 m/s

Speed of Sound in Water

Approximately 1,480 m/s

Type of Wave Sound Is

Sound is a longitudinal wave

Wavelength vs Frequency

As wavelength increases, frequency decreases

Speed of Sound Formula

Speed = Wavelength × Frequency

Doppler Effect

A change in observed frequency due to motion of the source or observer

Why You Hear Beats

Beats occur when two close frequencies interfere with each other

Rarefaction

The low-pressure region of a sound wave

Compression

The high-pressure region of a sound wave

Standing Wave

Caused by interference of two waves traveling in opposite directions

Purpose of Simple Machines

Simple machines reduce the amount of force needed to do work

Mechanical Advantage

The ratio of output force to input force

Lever

A rigid bar that rotates around a fulcrum

Efficiency

The ratio of useful output work to input work

Relationship of Quantities

Kinetic energy depends on mass and velocity squared

Tripling Velocity and Kinetic Energy

Kinetic energy increases by a factor of 9

Galileo’s Discovery

Objects fall at the same rate regardless of mass (ignoring air resistance)

Projectile Motion Acceleration

The vertical acceleration is always due to gravity (−9.8 m/s²)

Time in the Air of a Projectile

Determined by the vertical motion

Projectile Path

The path is called a parabola

Horizontal and Vertical Components

Common factor is time

Angles with Same Range

Complementary angles (like 30° and 60°) produce the same range

Perihelion vs Aphelion

Perihelion is closest to the sun; aphelion is farthest

Satellite in Orbit

A satellite is constantly falling toward the object it orbits