A train moves east at 30 m/s relative to the ground. A passenger walks west (backward) at 2 m/s relative to the train. What is the passenger's velocity relative to the ground?
A32 m/s east — the two velocities add because both are in the east direction
B28 m/s east — the train's velocity minus the walking velocity relative to the train
C2 m/s west — only the passenger's motion relative to the train matters
D30 m/s east — the walking velocity is too small to matter
Using Galilean velocity addition: v_passenger/ground = v_passenger/train + v_train/ground. The passenger walks west at 2 m/s relative to the train (−2 m/s east), and the train moves east at +30 m/s relative to the ground. So v_passenger/ground = −2 + 30 = +28 m/s east. The subscripts chain: v_person/ground = v_person/train + v_train/ground. The middle label (train) cancels, leaving person relative to ground. This chaining structure is the key to solving multi-body frame problems correctly.
Question 2 Multiple Choice
Two inertial frames F and G are moving at constant velocity relative to each other. An object accelerates at 5 m/s² in frame F. What is its acceleration in frame G?
A5 m/s² minus the relative velocity between the frames
B5 m/s² — acceleration is the same in all inertial frames
CIt depends on how fast F moves relative to G
DWe cannot determine the acceleration in G without knowing the object's mass
When two frames move at constant relative velocity (neither accelerating), acceleration is the same in both frames. Differentiating the velocity addition rule v_AG = v_AF + v_FG with respect to time: if v_FG is constant, its derivative is zero, so a_AG = a_AF. This is the key physical content of Galilean relativity: because F = ma and acceleration is frame-independent (for inertial frames), Newton's second law takes the same form in every inertial frame. Only velocity is frame-dependent, not acceleration.
Question 3 True / False
The velocity of an object is only meaningful when specified relative to a particular reference frame.
TTrue
FFalse
Answer: True
Velocity is inherently relational — it describes motion relative to some observer or coordinate system. The statement 'the car moves at 60 km/h' is incomplete without specifying 'relative to the ground' or 'relative to another car.' This is not a pedantic distinction: in problems with multiple moving bodies, failing to track which frame a velocity belongs to is the most common source of errors. There is no 'absolute' velocity in classical mechanics — only velocity relative to something.
Question 4 True / False
In an inertial reference frame, forces acting on an object have different magnitudes than in another inertial frame moving at constant velocity.
TTrue
FFalse
Answer: False
Forces and accelerations are identical in all inertial frames. Only velocities differ between inertial frames — and forces (F = ma) depend on acceleration, not velocity. This is precisely why Galilean relativity holds for mechanics: no mechanical measurement of force or acceleration can distinguish one inertial frame from another. The frame-dependence of velocity is observable (the Doppler effect, for example), but force measurements give the same result in every inertial frame.
Question 5 Short Answer
Why is it essential to be explicit about which reference frame each velocity is measured in before applying the Galilean velocity addition rule?
Think about your answer, then reveal below.
Model answer: The addition rule v_AG = v_AF + v_FG only works correctly when all velocities are expressed in the right frames. Mixing frames — treating part of a velocity as if it were in one frame and part in another — gives wrong answers. For example, treating a ball's speed relative to a thrower as if it were already relative to the ground, then adding the thrower's ground velocity, double-counts. Explicit frame labels (subscripts) ensure the middle frame cancels correctly, producing the velocity of one object relative to the intended frame.
Frame mixing is the most common error in relative-motion problems. The fix is always to write out the subscripts: what is the velocity of (A) relative to (B)? Then identify which pieces of information you have and check that the subscripts chain correctly. Once the labeling is right, the arithmetic is straightforward. The conceptual discipline of always asking 'relative to what?' carries forward into all of physics, including special relativity.