A spaceship is moving away from a star at a speed of $0.2c$. 

An observer in the spaceship will measure the speed at which light from the star is received to be:

:br

::indent
- A. $\hspace{1em}  $ $0.2c$

- B. $\hspace{1em}  $ $0.8c$

- C. $\hspace{1em}  $ $c$

- D. $\hspace{1em}  $ $1.2c$

Observations of muon decay can be used as evidence of 

::indent
- :::tableoptions{col1="hide" col2="hide"}
  | | |
  | :-- | :-- |
  | I. | Time dilation   |
  | II. | Length contraction |
  | III. | Absolute simultaneity |
  :::
:br
::indent
- A. $\hspace{1em}  $ I only


- B. $\hspace{1em}  $ II only


- C. $\hspace{1em}  $ I and II only


- D. $\hspace{1em}  $ II and III only

Two cyclists, $A$ and $B$, start riding their bicycles from the same point. Cyclist $A$ moves northwards with a speed of $4v$ relative to the ground, and cyclist $B$ moves westwards with a speed of $3v$ relative to the ground. 
 
:::center
![PH0721aa](question:4dfd2986-0848-4988-a8d9-ae8aea83249a)
:::


The magnitude of the velocity of the Cyclist $A$ relative to the Cyclist $B$ is

::indent
- A. $\hspace{1em}  v$ 


- B. $\hspace{1em}  4v$ 


- C. $\hspace{1em}  5v$ 


- D. $\hspace{1em}  7v$ 



\[Maximum mark: 10\]

1. A muon is created in a high-energy cosmic ray interaction in Earth’s upper atmosphere. The lifetime of the muon before decay is $2.3\times{10}^{-6}\, s$ in its frame of reference. The lifetime of the muon is measured as $11\times{10}^{-6}\, s$ from the perspective of an observer on Earth.    

    1. State and explain which of the given lifetimes is the proper time. :marks[2]

    2. Show that, according to the theory of special relativity, the speed of the muon is around $0.98\ c$. :marks[2] 

    3. 	Muons are likely created at $10\ km$ above the earth’s surface. Most of the muons are detected on the surface of the Earth. Explain how this observation can be interpreted as proof of special relativity. :marks[2]

2. A space-time diagram shows a motion of a muon in the frame of reference of a stationary observer at the place where the muon is created.

    :::center
    ![PH0667](question:0e46bcd0-6dcc-42e6-900d-590b9078085c)
    :::

    1. By using the information in (a)(ii), calculate the angle $\theta$ shown on the graph. :marks[2]

    2. Another muon is created a few kilometres below the muon in (b)(i) at the same time. It is moving at 0.75$c$. Draw the worldline of the second muon on the graph in (b)(i) according to the same observer. :marks[2]

Two inertial reference frames $S$ and $S'$ are moving at a speed $0.80c$ with respect to each other. The frames are such that when clocks in both frames show zero, the origins of the two frames coincide.

An event is observed to have space-time coordinates in the reference frame S as follows:
:::center
$x = 30\,m \hspace{5em} t=0.1\, \mu s$
:::

Which of the following best describes the spatial coordinate of the event in the reference frame $S'$?

:br

::indent
- A. $\hspace{1em}  $ $10\,m$

- B. $\hspace{1em}  $ $15\,m$

- C. $\hspace{1em}  $ $20\,m$

- D. $\hspace{1em}  $ $25\,m$

A spacecraft moving at $0.50c$ relative to the earth is travelling towards a distant planet which is $10.0\,ly$ away as measured from the earth.

Which of the following best describes the time taken to travel from the earth to the distant planet as measured by an observer inside the spacecraft?

:br

::indent
- A. $\hspace{1em}  $ 11.5 years

- B. $\hspace{1em}  $ 12.0 years

- C. $\hspace{1em}  $ 17.3 years

- D. $\hspace{1em}  $ 20.0 years

A spacecraft passes by a space station. The spacecraft is moving at speed $v$ relative to the space station Observers on the spacecraft measure the station to have a length of $250\,m$. 

An astronaut inside the station measures its length to be $255\,m$. 

Which of the following best describes the value of $v$?

:br

::indent
- A. $\hspace{1em}  $ $0.04c$

- B. $\hspace{1em}  $ $0.20c$

- C. $\hspace{1em}  $ $0.80c$

- D. $\hspace{1em}  $ $0.98c$


At a relativistic speed, a rocket journeyed from Earth to Saturn. The duration of the travel is measured according to the stationary observer on earth as $t$. The length of the rocket is measured according to the observer in the rocket as $L$.  Which of the following is correct for the time of travel according to the observer in the rocket and the length of the rocket according to the observer on the Earth?

:br


:::tableoptions{col1="hide"}
| | Time of travel (rocket observer) | Length of the rocket (Earth observer) |
| :-: | :-: | :-: |
| $\hspace{1.5em}$A.$\hspace{1.5em}$| Less than $t$ |Shorter than $L$ |
|$\hspace{1.5em}$B.$\hspace{1.5em}$ | Less than $t$| Longer than $L$ |
| $\hspace{1.5em}$C.$\hspace{1.5em}$ | Greater than $t$ | Shorter than $L$ |
| $\hspace{1.5em}$D.$\hspace{1.5em}$ | Greater than $t$ | Longer than $L$ |

[Maximum mark: 11]

1. In a thought experiment, a spacecraft recedes away from the Earth at a constant speed of  0.92$c$ in the reference frame of Earth. The length of the spacecraft is measured as 35$\, m$ by an observer in the spacecraft.

    :::center
    ![PH0666](question:8a42c781-cb30-4046-bfdc-ea70ceacf328)
    :::

    1. State the differences between Galilean and Special relativity with regards to the speed of light and time. :marks[2]

    2. Calculate the length of the spacecraft measured by an observer on Earth. :marks[3]

2. After some time, the spacecraft encounters a rocket that moves at a speed of 0.75$c$ relative to Earth in the opposite direction.                          

    1. Show that, relative to the spacecraft, the speed of the rocket according to the Galilean transformation is around 1.6$c$. :marks[2]

    2. Calculate, relative to the spacecraft, the speed of the rocket according to the Lorentz transformation. :marks[2]
    
    3. According to postulates of special relativity, outline which of your calculations in (b)(i) and (b)(ii) related to the speed of the rocket relative to the spacecraft is valid. :marks[2]

Which of the following postulates has the consequence of time and space not being absolute? 

::indent
- A. $\hspace{1em}  $Newton's laws of motion are the same in all reference frames


- B. $\hspace{1em}  $The relative velocity of two inertial frames of reference is constant


- C. $\hspace{1em}  $The laws of physics are the same in all inertial reference frames


- D. $\hspace{1em}  $The speed of light in a vacuum is constant in all inertial reference frames

A spaceship is moving at a constant velocity relative to a station. The spacetime diagram shows the worldline of the spaceship in the frame of reference of the station. 
:::center
![PH0727](question:35936b18-cefd-4add-8427-9c45859dcd1e)
:::

 
Which of the following gives the speed of the spaceship in terms of $c$?

::indent
- A. $\hspace{1em}  the\ shaded\ area$


- B. $\hspace{1em}  	\dfrac{1}{The\ shaded\ area}$ 


- C. $\hspace{1em}  	tan\theta$ 


- D. $\hspace{1em}  	\dfrac{1}{tan\theta}$ 


In a distant future, an area with dimensions of $2.0\, ly$ and $5.0\, ly$, as measured by a stationary observer on Earth, is reserved for a spaceship road. The diagram illustrates the area and the direction of motion for a spaceship moving at a speed of $0.6c$.

:::center
![PH0726](question:9f8c0308-4d6f-4df5-aacc-99b6475dfa83)
:::


What is the area of the road from the perspective of the observer in the spaceship? 

::indent
- A. $\hspace{1em}  	6.4\, {ly}^2$ 


- B. $\hspace{1em}  	8.0\, {ly}^2$ 


- C. $\hspace{1em}  	10\, {ly}^2$ 


- D. $\hspace{1em}  	13\, {ly}^2$ 



[Maximum mark: 14\]

1. Car **A** and Car **B** are travelling in the same direction along a straight line. In the reference frame of a stationary observer on the ground, Car **A** has a speed of  $24 \, m\,s^{-1}$ and Car **B** has a speed of $36 \, m\,s^{-1}$.

    :::center
    ![PH0671a](question:9f937be0-eb02-4371-9918-16ea71ca4e8a)
    :::

    1. Explain what is meant by a frame of reference. :marks[2]

    2. Calculate the velocity of Car **B** relative to the stationary observer in Car **A**. :marks[2]

    3. The distance travelled by Car **B** relative to Car **A** is $60\, m$ in a time interval of $5.0\, s$. Use the galilean transformation equation to calculate the distance travelled by Car **B** relative to the stationary observer on the ground for the same time interval. :marks[2]

:br

2. Now consider two spaceships, **C** and **D**, traveling through space towards a planet.

    :::center
    ![Screenshot 2023-07-29 at 9.09.10 AM](question:6218d24c-4793-41ec-ba3d-0c4ebbbba52b)
    :::

    Both of the spaceships turn on their lights. The turning on of the lights of spaceship **C** and the turning of the lights of spaceship **D** are defined as Events **C** and **D** respectively. Event **C** has coordinates $x_C = 3.456 \times {10}^5 \, m$, $t_C=0\, s$ and event **D** has coordinates $x_D = 3.443 \times {10}^5 \, m$,  $t_D = 1.1 \times {10}^{-3} \, s$ according to a stationary observer on the planet. 

    A rocket flies towards the two spaceships at a speed of $0.85\ c$ according to the same observer. 

    1. According to the frame of reference of the rocket, determine the space differences between events **C** and **D**. :marks[3]

    2. According to the frame of reference of the rocket, determine the space-time interval between events **C** and **D**. :marks[3]

    3. Discuss whether Event **C** and Event **D** can occur at the same time according to some other inertial frame. :marks[2]
    

A spaceship is moving at a speed of $0.80 c$ relative to a stationary observer on Earth. An event occurring in the spaceship is measured by an observer in the spaceship to have a duration of $12\, s$. What is the duration of the event as measured by the stationary observer on Earth?

::indent
- A. $\hspace{1em}  	7.2\, s$ 


- B. $\hspace{1em}  	12\, s$ 


- C. $\hspace{1em}  	15\, s$ 


- D. $\hspace{1em}  	20\, s$ 

A spacecraft travelling at a $0.40c$, away from the earth launches  a probe forward  also in the direction away from earth, at $0.30c$ relative to the spaceship.

Which of the following best describes the speed of the probe relative to earth?

:br

::indent
- A. $\hspace{1em}  $ $0.58c$

- B. $\hspace{1em}  $ $0.63c$

- C. $\hspace{1em}  $ $0.70c$

- D. $\hspace{1em}  $ $0.75c$


In a landing zone designed for spaceships that can move at relativistic speeds, a sequence of warning lights A, B, C, and D are used to guide landings. The spacetime diagram of this system shows the lights at rest in a particular reference frame and the worldline of a spaceship approaching the landing zone.
 
:::center

![PH0725](question:e5b48fe4-b1a1-482d-bee6-615e9da6338e)
:::





Which of the following is the order of the lights reaching an observer on the spaceship from warning lights?

::indent
- A. $\hspace{1em}  	A,\ D,\ C,\ B$ 


- B. $\hspace{1em}  	D,\ C,\ B,\ A$ 


- C. $\hspace{1em}  	B,\ C,\ A,\ D$ 


- D. $\hspace{1em}  	A,\ C,\ B,\ D$ 

Reference Frames, Galilean Relativity, Special Relativity, Lorentz Transformations, Space-Time Diagrams, Simultaneity

HL - 2025

Space, Time & Motion

A.1 Uniform Acceleration

PH0123

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A.1 Motion Graphs

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PH0572

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PH0644

A.4 Rotational Mechanics

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PH1056

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PH0700

PH0707

PH1057

PH0741

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PH1052

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PH0615

A.5 Special Relativity

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PH0728

PH0722

PH0723

PH0727

PH0726

PH0724

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PH0667

Displacement, Velocity, Acceleration, Uniform Acceleration Equations, Projectile Motion

Kinematics

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PH0511

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Forces, Free-Body Diagrams, Newton's Laws, Friction, Equilibrium, Momentum, Impulse, Collisions, Circular Motion

IB Physics HL - 2025 - Questionbank

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