Graphs of Motion

Test yourself

Displacement-Time Graphs

Displacement-time graphs have displacement on the y-axis and time on the x-axis.

Gradient

If the object is not accelerating (travelling at a constant velocity), then the graph will be a straight line.
The gradient of a graph is defined as the change in y divided by the change in x.
On a displacement-time graph, y is the displacement and x is the time, so the gradient is the velocity:
- Gradient $=\frac{\Delta y}{\Delta x} = \frac{\Delta s}{\Delta t} = v$

Uniform acceleration

An object under uniform (constant) acceleration will have a displacement-time graph that curves upwards.
This is because the velocity (and therefore the gradient) is increasing.
The larger the acceleration, the faster the graph curves upwards.
If the object is decelerating, the velocity increases more slowly, so the graph becomes less steep.

Stationary

The graph of a stationary object is a horizontal line.
- The gradient of the graph is equal to zero as the average velocity of the object is zero.

Instantaneous and average velocity

To find the instantaneous velocity, draw a tangent to the curve at the point of interest and calculate its gradient.
The gradient of the tangent is the gradient of the curve at that point and therefore the velocity at that point.
To find the average velocity, simply divide the total change in displacement by the total time.

Instantaneous and average velocity

Velocity-Time Graphs

Velocity-time graphs have velocity on the y axis and time on the x axis.

Gradient

The gradient of a graph is defined as the change in y divided by the change in x.
On a velocity-time graph, y is the velocity and x is the time, so the gradient is the acceleration:
- gradient $=\frac{\Delta y}{\Delta x} = \frac{\Delta v}{\Delta t} = a$

Area under the graph

The area under a velocity-time graph is the displacement of the object.

Non-uniform acceleration

The graph above shows what a velocity-time graph looks like for non-uniform acceleration.

Acceleration-Time Graphs

Acceleration-time graphs have acceleration on the y-axis and time on the x-axis.

Uniform acceleration

If the graph is positive, the object is accelerating.
If the graph is negative, the object is decelerating.
If the graph is at zero, there is no acceleration.
- This means that the object is stationary or moving with constant velocity.

Area under the graph

The area under an acceleration-time graph gives the object's change in velocity.

Non-uniform acceleration

Any line on an acceleration-time graph that is not horizontal indicates a non-uniform acceleration.
This acceleration can be increasing or decreasing.
In this case, the object's acceleration decreases towards the ends of its motion.
- Note that this is not the same as the object decelerating.

1Space, Time & Motion

1.1Motion

1.1.1Motion Basics

1.1.2Graphs of Motion

1.1.3Uniform Acceleration Equations

1.1.4Projectile Motion

1.1.5Bouncing Ball Example

1.2Forces

1.2.1Friction

1.2.2Terminal Speed

1.2.3Newton's Laws

1.2.4Exam-Style Question - Forces

1.2.5End of Topic Test - Newton's Third Law

1.3Momentum & Impulse

1.3.1Momentum

1.3.2Momentum 2

1.3.3End of Topic Test - Newton's Laws & Momentum

1.4Work, Energy & Power

1.4.1Work & Energy

1.4.2Conservation of Energy

1.4.3Power & Efficiency

1.4.4IB Multiple Choice- Work, Energy & Power

2The Particulate Nature of Matter

2.1Thermal Concepts

2.1.1Molecular Kinetic Theory Model

2.1.2Molecular Kinetic Theory Model 2

2.1.3Thermal Energy Transfer

2.1.4Thermal Energy Transfer Experiments

2.1.5Thermal Equilibrium

2.1.6Thermal Conductivity

2.1.7Heat Energy Transfer

2.2Modelling a Gas

2.2.1Ideal Gases

2.2.2Ideal Gases 2

2.2.3End of Topic Test - Thermal Energy & Ideal Gases

2.2.4Exam-Style Question - Ideal Gases

3Wave Behaviour

3.1Oscillations

3.1.1Progressive Waves

3.1.2Simple Harmonic Motion

3.2Travelling Waves

3.2.1Wave Speed & Phase Difference

3.2.2Longitudinal & Transverse Waves

3.2.3Electromagnetic Waves

3.2.4Electromagnetic Waves 2

3.2.5Sound Waves

3.3Wave Characteristics

3.3.1Polarisation

3.4Wave Behaviour

3.4.1Reflection & Absorption

3.4.2Reflection of Light

3.4.3Refraction

3.4.4Refractive index

3.5Standing Waves

3.5.1Standing Waves

3.5.2Standing Waves 2

3.5.3End of Topic Test - Standing Waves

3.5.4IB Multiple Choice - Waves

3.6Simple Harmonic Motion

3.6.1Simple Harmonic Motion

3.6.2Simple Harmonic Systems

3.6.3Energy in Simple Harmonic Motion

3.6.4End of Topic Test - Simple Harmonic Motion

3.6.5End of Topic Test - Simple Harmonic Motion

3.7Single Slit Diffraction

3.7.1Diffraction

3.8Interference

3.8.1Interference

3.8.2Interference 2

3.8.3Diffraction Gratings

3.8.4End of Topic Test - Diffraction

3.9Doppler Effect

3.9.1Doppler Effect

4Fields

4.1Circular Motion

4.1.1Circular Motion

4.1.2Centripetal Force

4.1.3IB Multiple Choice - Circular Motion

4.2Newton's Law of Gravitation

4.2.1Newton's Law

4.2.2Orbits of Planets & Satellites

4.2.3Escape Velocity & Synchronous Orbits

4.2.4End of Topic Test - Gravitational Fields

4.3Fields

4.3.1Fields

4.3.2Gravitational Field Strength

4.3.3Gravitational Potential

4.3.4Electric Field Strength

4.3.5Electrostatic & Gravitational Forces

4.3.6Electric Potential

4.3.7IB Multiple Choice - Gravitational Fields

4.4Fields at Work

4.4.1Radial Field Strength

4.4.2Orbits of Planets & Satellites

4.4.3Escape Velocity & Synchronous Orbits

4.4.4End of Topic Test - Gravitational Fields

4.4.5Uniform Electric Fields

4.4.6IB Multiple Choice - Electric Field & Potential

4.5Electric Fields

4.5.1Electric Charge

4.5.2Conservation of Charge

4.5.3Coulomb's Law

4.5.4Current

4.5.5Potential Difference

4.5.6IB Multiple Choice - Electric Charge

4.6Magnetic Effect of Electric Currents

4.6.1Magnetism

4.6.2Magnetic Field

4.6.3Magnetic Force

4.6.4Moving Charges in a Magnetic Field

4.6.5IB Multiple Choice - Magnetism

4.7Heating Effect of Currents

4.7.1Circuits

4.7.2Resistance

4.7.3Power and Conservation

4.7.4IB Multiple Choice - DC Circuits

4.8Electromagnetic Induction

4.8.1Electromagnetic Induction

4.8.2Electromagnetic Induction 2

4.8.3Magnetic Flux & Flux Linkage

4.8.4End of Topic Test - Electromagnetic Induction

4.9Power Generation & Transmission

4.9.1Alternating Currents

4.9.2Operation of a Transformer

4.10Capacitance

4.10.1Capacitance

4.10.2Parallel Plate Capacitor

4.10.3Energy Stored by a Capacitor

4.10.4Capacitor Discharge

4.10.5Capacitor Charge

4.10.6Magnetic Flux Density

4.10.7End of Topic Test - Capacitance & Flux Density

5Nuclear & Quantum Physics

5.1Discrete Energy & Radioactivity

5.1.1Atomic Spectra

5.1.2Atomic Structure

5.1.3Photons

5.1.4Discrete Energy Levels

5.1.5Alpha, Beta & Gamma Radiation

5.1.6Scientific Practices - Unstable Nuclei

5.1.7Radioactive Decay

5.1.8IB Multiple Choice - Atomic Physics

5.2Nuclear Reactions

5.2.1Mass & Energy

5.2.2Nuclear Fission

5.3The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons

5.3.2Particle Interactions

5.3.3Classification of Particles

5.3.4Wave-Particle Duality

5.3.5Wave Functions & Probability

5.3.6IB Multiple Choice - Quantum Physics

5.4Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay

5.4.2Nuclear Radius

5.4.3IB Multiple Choice - Nuclear Physics

6Measurements

6.1Measurements & Errors

6.1.1Fundamental Units

6.1.2SI Prefixes, Standard Form & Converting Units

6.1.3End of Topic Test - Units & Prefixes

6.2Uncertainties & Errors

6.2.1Limitation of Physical Measurements

6.2.2Uncertainty

6.2.3Estimation

6.2.4End of Topic Test - Measurements & Errors

6.3Vectors & Scalars

6.3.1Scalars & Vectors

6.3.2Vector Problems

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