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 𝑆. 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 𝑆. 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 𝑆. 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 𝑆. Which diagram shows a particle that moves at a constant nonzero speed in 𝑆 for the entirety of its world line?

  • A
  • B
  • C
  • D
  • E

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

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

  • A
  • B
  • C
  • D
  • E

Q7:

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

  • A
  • B
  • C
  • D

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

The given Minkowski diagram shows two inertial frames: frame 𝑆 with axes 𝑥 and 𝑐𝑡 and frame 𝑆 with axes 𝑥 and 𝑐𝑡. 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 𝑆
  2. The world line of an object that is at rest in frame 𝑆
  3. The world line of an object that is moving at the speed of light, 𝑐, in both 𝑆 and 𝑆
  4. The world line of an object that is at rest in frame 𝑆
  5. A line of constant time in 𝑆
  6. A line of constant time in 𝑆
  7. The world line of an object that is moving at a nonconstant speed in both 𝑆 and 𝑆
  8. The world line of an object that is moving at a constant speed in 𝑆
  • Aiv and viii
  • Bi and ii
  • Cviii and vi
  • Diii and iv
  • Ev and vi

Q10:

The Minkowski diagram shows three inertial frames: frame 𝑆 with axes 𝑥 and 𝑐𝑡, frame 𝑆 with axes 𝑥 and 𝑐𝑡, and frame 𝑆 with axes 𝑥 and 𝑐𝑡. The red line shows the world line of a particle.

What is the speed of the particle in frame 𝑆?

  • A𝑐2
  • B𝑐2
  • C𝑐
  • D𝑐4
  • E𝑐3

What is the speed of the particle in frame 𝑆?

  • A𝑐3
  • B𝑐4
  • C𝑐
  • D𝑐2
  • E𝑐2

Q11:

The Minkowski diagram shows three inertial frames: frame 𝑆 with axes 𝑥 and 𝑐𝑡, frame 𝑆 with axes 𝑥 and 𝑐𝑡, and frame 𝑆 with axes 𝑥 and 𝑐𝑡. The red line shows the world line of a particle. In which inertial frame is the particle at rest?

  • A𝑆
  • B𝑆
  • C𝑆

Q12:

The Minkowski diagram shows three inertial frames: frame 𝑆 with axes 𝑥 and 𝑐𝑡, frame 𝑆 with axes 𝑥 and 𝑐𝑡, and frame 𝑆 with axes 𝑥 and 𝑐𝑡. The red line shows the world line of a particle.

In which inertial frame does the particle have the greatest speed?

  • A𝑆
  • B𝑆
  • C𝑆

In which inertial frame is the particle at rest?

  • A𝑆
  • B𝑆
  • C𝑆

Q13:

The above Minkowski diagram shows three inertial frames: frame 𝑆 with axes 𝑥 and 𝑐𝑡, frame 𝑆 with axes 𝑥 and 𝑐𝑡, and frame 𝑆 with axes 𝑥 and 𝑐𝑡. Which frame has the greatest speed relative to 𝑆?

  • A𝑆
  • B𝑆

Q14:

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

  1. A line of constant time in 𝑆
  2. The world line of an object that is moving at the speed of light, 𝑐, in both 𝑆 and 𝑆
  3. The world line of an object that is at rest in frame 𝑆
  4. The world line of an object that is moving at a constant speed in 𝑆
  5. A line of constant time in 𝑆
  6. The world line of an object that is moving at a constant speed in 𝑆
  7. The world line of an object that is moving at a nonconstant speed in both 𝑆 and 𝑆
  8. The world line of an object that is at rest in frame 𝑆
  • Ai and ii
  • Biv and vi
  • Civ and vii
  • Dviii and v
  • Eiii and vi

Q15:

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

  • A𝑆
  • B𝑆
  • C𝑆

Q16:

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

  1. A line of constant time in 𝑆
  2. The world line of an object that is moving at the speed of light, 𝑐, in both 𝑆 and 𝑆
  3. The world line of an object that is at rest in frame 𝑆
  4. The world line of an object that is moving at a constant speed in 𝑆
  5. A line of constant time in 𝑆
  6. The world line of an object that is moving at a constant speed in 𝑆
  7. The world line of an object that is moving at a nonconstant speed in both 𝑆 and 𝑆
  8. The world line of an object that is at rest in frame 𝑆
  • Aiii
  • Bvi
  • Cii
  • Dvii
  • Eiv

Q17:

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

  • A
  • B
  • C
  • D
  • E

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