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Physics / Chapter 2: Motion Along a Straight Line / Section 2-1

Motion — Question 1

Section 2-1 · Physics pages 132–133

Question 1 At rest relative to what? A straight station platform has fixed metre marks increasing eastward. At three successive instants, observers record the marks alongside a train seat, a passenger’s badge, and a platform sign: The successive seat readings are 10, 20, 30 m; badge readings are 13, 23, 33 m; sign readings are 12, 12, 12 m, as plotted below. The platform marks are a fixed reference. The readings are exact in this model and all three objects remain on the same east–west line. No observations between these instants are supplied. “At rest relative to a reference” means retaining the same location in that reference throughout the interval being discussed. First 10 13 Second 20 23 Third 30 33 Filled: seat; open: badge; tick: sign at 12 m. Recorded platform positions (m), east to the right; no intervening motion is drawn. (a) Which tracked points definitely moved relative to the platform between recorded instants? Which point is compatible with rest relative to it? (b) Compare the badge’s location relative to the seat at all three instants. Are the statements “the passenger moved” and “the passenger stayed in the same place” necessarily contradictory? Rewrite them with precise reference and time qualifications. (c) Describe how the platform sign changes location relative to the seat across the observations. Explain why a sign fixed to the platform need not be at rest in a train-based description. (d) Do these samples prove that the badge stayed at rest relative to the seat at every intervening instant? Give a possible unobserved history and state what extra evidence would rule it out.
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Question 1 - Solution At rest relative to what? First 10 13 Second 20 23 Third 30 33 Filled: seat; open: badge; tick: sign at 12 m. (a) Use one declared reference for the comparison. ∆xseat = (10, 10) m, ∆xbadge = (10, 10) m, ∆xsign = (0, 0). The seat is beside different platform marks, 10, 20, and 30; the badge is beside 13, 23, and 33. Both definitely changed location relative to the platform. The sign has the same recorded mark, 12, so the samples are compatible with platform rest. Samples alone do not prove constancy between observations. (b) The same passenger can have different motion descriptions. Write xB, xS, xG for the badge, seat and sign coordinates. xB/S = xB −xS : (13 −10, 23 −20, 33 −30) = (3, 3, 3) m. At every recorded instant, the badge is 3 m east of the seat: 13 −10 = 23 −20 = 33 −30 = 3. Valid statements are: • The badge changed location relative to the platform between the recorded instants. • The badge had the same location relative to the seat at those instants. These claims use different references and are consistent. The second is deliberately limited to the sampled instants; it does not yet establish continuous rest relative to the seat. (c) A reference tied to the train changes the sign’s description. xG/S = xG −xS : (12 −10, 12 −20, 12 −30) = (2, −8, −18) m. Initially the sign is 2 m east of the seat. At the second observation it is 8 m west of the seat, and at the third it is 18 m west. Thus its recorded location changes westward in the seat-based description. Being fixed to the platform does not make it fixed relative to the train. (d) A repeated relation at samples is not a continuous record. Between observations, the passenger could walk away from the seat and return to the same relative location before the next sample. All recorded numbers would remain unchanged. A stipulated fixed attachment, or sufficiently informative continuous observation of the badge relative to the seat, could rule out such a history within the observation model. A motion statement needs both a reference and a stated interval or set of observations. The word “moving” by itself omits part of the physical description.

Question 1

At rest relative to what?

A straight station platform has fixed metre marks increasing eastward. At three successive instants, observers record the marks alongside a train seat, a passenger’s badge, and a platform sign: The successive seat readings are 10,20,30m10,20,30\ \mathrm{m}; badge readings are 13,23,33m13,23,33\ \mathrm{m}; sign readings are 12,12,12m12,12,12\ \mathrm{m}, as plotted below. The platform marks are a fixed reference. The readings are exact in this model and all three objects remain on the same east–west line. No observations between these instants are supplied. “At rest relative to a reference” means retaining the same location in that reference throughout the interval being discussed.

Diagram shown in the original SVG worksheet.

  1. Which tracked points definitely moved relative to the platform between recorded instants? Which point is compatible with rest relative to it?

  2. Compare the badge’s location relative to the seat at all three instants. Are the statements “the passenger moved” and “the passenger stayed in the same place” necessarily contradictory? Rewrite them with precise reference and time qualifications.

  3. Describe how the platform sign changes location relative to the seat across the observations. Explain why a sign fixed to the platform need not be at rest in a train-based description.

  4. Do these samples prove that the badge stayed at rest relative to the seat at every intervening instant? Give a possible unobserved history and state what extra evidence would rule it out.

Question 1 - Solution

At rest relative to what?

Diagram shown in the original SVG worksheet.

(a) Use one declared reference for the comparison.

Δxseat=(10,10)m,Δxbadge=(10,10)m,Δxsign=(0,0).\Delta x_{\mathrm{seat}}=(10,10)\ \mathrm{m},\quad\Delta x_{\mathrm{badge}}=(10,10)\ \mathrm{m},\quad\Delta x_{\mathrm{sign}}=(0,0).

The seat is beside different platform marks, 10, 20, and 30; the badge is beside 13, 23, and 33. Both definitely changed location relative to the platform. The sign has the same recorded mark, 12, so the samples are compatible with platform rest. Samples alone do not prove constancy between observations.

(b) The same passenger can have different motion descriptions.

Write xB,xS,xGx_B,x_S,x_G for the badge, seat and sign coordinates. xB/S=xB−xS:(13−10,23−20,33−30)=(3,3,3)m.x_{B/S}=x_B-x_S:\quad(13-10,23-20,33-30)=(3,3,3)\ \mathrm{m}.

At every recorded instant, the badge is 3m\boxed{3\ \mathrm{m}} east of the seat: 13−10=23−20=33−30=313-10=23-20=33-30=3. Valid statements are:

  • The badge changed location relative to the platform between the recorded instants.

  • The badge had the same location relative to the seat at those instants.

These claims use different references and are consistent. The second is deliberately limited to the sampled instants; it does not yet establish continuous rest relative to the seat.

(c) A reference tied to the train changes the sign’s description.

xG/S=xG−xS:(12−10,12−20,12−30)=(2,−8,−18)m.x_{G/S}=x_G-x_S:\quad(12-10,12-20,12-30)=(2,-8,-18)\ \mathrm{m}.

Initially the sign is 2 m east of the seat. At the second observation it is 8 m west of the seat, and at the third it is 18 m west. Thus its recorded location changes westward in the seat-based description. Being fixed to the platform does not make it fixed relative to the train.

(d) A repeated relation at samples is not a continuous record.

Between observations, the passenger could walk away from the seat and return to the same relative location before the next sample. All recorded numbers would remain unchanged. A stipulated fixed attachment, or sufficiently informative continuous observation of the badge relative to the seat, could rule out such a history within the observation model.

A motion statement needs both a reference and a stated interval or set of observations. The word “moving” by itself omits part of the physical description.

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