QCAA Physics Alternative Sequence Special relativity

Because Observer 2 measures the train to be shorter than the tunnel, the train will fully enter the tunnel before its front exits, meaning these events are not simultaneous.

The train's mass is an invariant property (rest mass) or depends only on its speed (relativistic mass), neither of which changes simply by entering the tunnel.

The train is traveling at a constant relativistic speed; entering the tunnel does not exert a force to cause it to accelerate.

This is incorrect because an accelerating object represents a non-inertial frame of reference. By definition, an inertial frame must have zero acceleration.

This is incorrect because turning a corner involves a change in direction, which means the car is experiencing centripetal acceleration. Even at a constant speed, a change in direction makes it a non-inertial frame of reference.

This is incorrect because the roller-coaster is speeding up, meaning its velocity is changing and it is accelerating. Any accelerating environment is a non-inertial frame of reference.

Incorrect. This is the formula for gravitational potential energy, where $g$ is the acceleration due to gravity and $h$ is height.

Incorrect. This incorrectly combines the structure of the kinetic energy formula with the speed of light ($c$), which does not represent any standard physical relationship.

Incorrect. This is the classical formula for kinetic energy, representing the energy of an object in motion with mass $m$ and velocity $v$.

This result comes from incorrectly omitting the squares on the velocities, calculating $\frac{1}{\sqrt{1 - v/c}}$ instead of the proper Lorentz factor formula.

This is the value of $\gamma^2$ (approximately $3.27$), which occurs if you forget to take the square root of the denominator in the Lorentz factor formula.

This is an incorrect value resulting from a miscalculation. The correct Lorentz factor must be found using the formula $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$.

Length contraction only occurs parallel to the direction of motion, so the object's height would remain unchanged. Furthermore, length contraction is a consequence of relativistic speeds, not the limiting factor preventing an object from reaching the speed of light.

Time dilation means time passes slower for the moving object relative to a stationary observer, but it does not act as a physical drag force that decreases the object's velocity.

As an object approaches the speed of light, its resistance to acceleration (effective inertia) actually increases toward infinity, making it harder to accelerate, rather than decreasing.

An object cannot move relative to its own frame of reference; by definition, it is always stationary within its own frame.

The particle is moving at relativistic speeds relative to the stationary detector, meaning they are in completely different frames of reference.

The longer half-life is a real, measurable physical consequence of time dilation, not an error or limitation in observation.

If the object is in motion relative to the observer's frame of reference, the measured length will be shorter than the proper length due to length contraction.

Proper length is specifically defined in the object's rest frame. Measurements taken from an accelerating frame do not yield the proper length.

Even if the object is moving at a constant velocity, an observer in a different frame will measure a contracted length rather than the proper length.

This value is incorrect and does not follow the proper length contraction formula. The length must be divided by the Lorentz factor, not calculated using an incorrect relativistic relation.

This is the proper length of the beamline measured in the laboratory frame where it is at rest. The protons will observe a shorter, contracted length due to their relative motion.

This result comes from incorrectly multiplying the proper length by the Lorentz factor ($L = \gamma L_0$), which would represent length expansion rather than length contraction.

Incorrect. Travelling at a constant speed is insufficient because the direction could be changing (such as in circular motion), which implies acceleration. An inertial frame must travel at a constant velocity.

Incorrect. The definition of an inertial frame does not depend on its speed relative to the speed of light, $c$. A frame moving at a constant velocity close to $c$ is still a valid inertial frame.

Incorrect. The expansion of the universe is a cosmological phenomenon and does not define an inertial frame. Inertial frames are defined strictly by the absence of acceleration.