# Worksheet: World Lines in Minkowski Diagrams

In this worksheet, we will practice interpreting the world lines of objects in Minkowski diagrams.

Q1:

The following Minkowski diagrams show the world lines of different particles in an inertial frame . Four of the diagrams show only hypothetical world lines, as they show a particle that for part or all of its world line moves faster than the speed of light. Which diagram shows the world line of a particle that at no point moves faster than the speed of light?

• A • B • C • D • E Q2:

The following Minkowski diagrams show the world lines of different particles in an inertial frame . Which diagram shows a particle moving faster than the speed of light?

• A • B • C • D • E Q3:

The following Minkowski diagrams show the world lines of different particles in an inertial frame . Which diagram shows a particle that does not move at a constant speed?

• A • B • C • D • E Q4:

The following Minkowski diagrams show the world lines of different particles in an inertial frame . Which diagram shows a particle that moves at a constant nonzero speed in for the entirety of its world line?

• A • B • C • D • E Q5:

The following Minkowski diagrams show two inertial frames: frame with axes and and frame with axes and . In which diagram is the red line constant in time in frame ?

• A • B • C • D • E Q6:

The following Minkowski diagrams show two inertial frames: frame with axes and and frame with axes and . The red line shows the world line of a particle. Which diagram shows a particle that is not moving at a constant speed in ?

• A • B • C • D • E Q7:

The following Minkowski diagrams show the world lines of different particles in an inertial frame . Which diagram shows a particle that is at rest in ?

• A • B • C • D Q8:

The following Minkowski diagrams show an inertial frame . In which diagram is the red line constant in time in frame ?

• A • B • C • D • E Q9:

The given Minkowski diagram shows two inertial frames: frame with axes and and frame with axes and . Which two of the following does the red line in the diagram show?

1. The world line of an object that is moving at a constant speed in
2. The world line of an object that is at rest in frame
3. The world line of an object that is moving at the speed of light, , in both and
4. The world line of an object that is at rest in frame
5. A line of constant time in
6. A line of constant time in
7. The world line of an object that is moving at a nonconstant speed in both and
8. The world line of an object that is moving at a constant speed in • Aiv and viii
• Bi and ii
• Cviii and vi
• Diii and iv
• Ev and vi

Q10:

The Minkowski diagram shows three inertial frames: frame with axes and , frame with axes and , and frame with axes and . The red line shows the world line of a particle. What is the speed of the particle in frame ?

• A
• B
• C
• D
• E

What is the speed of the particle in frame ?

• A
• B
• C
• D
• E

Q11:

The Minkowski diagram shows three inertial frames: frame with axes and , frame with axes and , and frame with axes and . The red line shows the world line of a particle. In which inertial frame is the particle at rest? • A
• B
• C

Q12:

The Minkowski diagram shows three inertial frames: frame with axes and , frame with axes and , and frame with axes and . The red line shows the world line of a particle. In which inertial frame does the particle have the greatest speed?

• A
• B
• C

In which inertial frame is the particle at rest?

• A
• B
• C

Q13:

The above Minkowski diagram shows three inertial frames: frame with axes and , frame with axes and , and frame with axes and . Which frame has the greatest speed relative to ? • A
• B

Q14:

The given Minkowski diagram shows two inertial frames: frame with axes and and frame with axes and . Which two of the following does the red line in the diagram show? 1. A line of constant time in
2. The world line of an object that is moving at the speed of light, , in both and
3. The world line of an object that is at rest in frame
4. The world line of an object that is moving at a constant speed in
5. A line of constant time in
6. The world line of an object that is moving at a constant speed in
7. The world line of an object that is moving at a nonconstant speed in both and
8. The world line of an object that is at rest in frame
• Ai and ii
• Biv and vi
• Civ and vii
• Dviii and v
• Eiii and vi

Q15:

The Minkowski diagram shows three inertial frames: frame with axes and , frame with axes and , and frame with axes and . The red line shows the world line of a particle. In which inertial frame does the particle have the greatest speed? • A
• B
• C

Q16:

The Minkowski diagram shows two inertial frames: frame with axes and and frame with axes and . Which of the following does the red line in the diagram show? 1. A line of constant time in
2. The world line of an object that is moving at the speed of light, , in both and
3. The world line of an object that is at rest in frame
4. The world line of an object that is moving at a constant speed in
5. A line of constant time in
6. The world line of an object that is moving at a constant speed in
7. The world line of an object that is moving at a nonconstant speed in both and
8. The world line of an object that is at rest in frame
• Aiii
• Bvi
• Cii
• Dvii
• Eiv

Q17:

The following Minkowski diagrams show two inertial frames: frame with axes and and frame with axes and . The red line shows the world line of a particle. Which diagram shows a particle that is at rest in the frame ?

• A • B • C • D • E 