Physics Measurements, Graphs & Uncertainty — Practice · Grade 12 Science

Chapter: Measurement & Vector Foundations

What this practice covers

By the end of Physics Measurements, Graphs & Uncertainty you should be able to:

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: dimension, residual, resolution.

Problem 1

Trials are 1.8,2.0,2.2 s. Find mean.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

2 s

6/3=2.

Problem 2

What does a slope unit m/s² suggest?
Answer and explanation

Acceleration, if the vertical axis is velocity and horizontal time.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

Convert 450 milliseconds to seconds.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

0.45 s

450/1000=.450 s.

Problem 4

Convert 3.0 kJ to joules.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

3000 J

kilo means 1000.

Problem 5

A velocity–time line rises from 1 to 7 m/s in 3 s. Find slope and its meaning. Show the reasoning, not just the conclusion.
Hints

Check axis units: meters divided by seconds.

Answer and explanation

(7−1)/3=2 m/s², the acceleration.

Problem 6

Why report uncertainty when comparing two measured accelerations?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Differences smaller than relevant uncertainty may not support a confident physical distinction.

Problem 7

Calculator output is not additional measurement evidenceCalculator output is not additional measurement evidenceInputReported valueMeaningLength2.40 cmThree significant figuresWidth1.2 cmTwo significant figuresProduct2.9 cm²Round at the endUnrounded calculation: 2.40 × 1.2 = 2.88Digits alone are not a full uncertainty analysis.
Original precision example; significant-figure conventions and explicit uncertainty analysis are distinguished.
Interpret the supplied visual. Why is 2.88 cm² rounded to 2.9 cm² here, and what does that not establish?
Answer and explanation

The width has two significant figures. Rounding does not establish the interval’s confidence level or rule out a systematic error.

A reported number should reflect its measurement process. Classroom significant-figure rules summarize precision for basic arithmetic: multiplication follows the least significant-figure count, while addition follows decimal-place precision. They do not specify a complete probability distribution or identify calibration error. Retain extra calculation digits internally and round the final result. When a task supplies explicit uncertainty intervals, use those intervals and their assumptions rather than inventing uncertainty from the last displayed digit.

The width has two significant figures. Rounding does not establish the interval’s confidence level or rule out a systematic error.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

Two speeds are reported as 3.2 ± 0.3 m/s and 3.6 ± 0.3 m/s. Give their intervals, assess overlap and name one shared error repeated trials cannot remove.
Answer and explanation

The ranges are [2.9,3.5] and [3.3,3.9] m/s, overlapping from 3.3 to 3.5 m/s. These alone do not resolve a difference; a common timing calibration bias can persist through repeats.

The ranges are [2.9,3.5] and [3.3,3.9] m/s, overlapping from 3.3 to 3.5 m/s.

These alone do not resolve a difference; a common timing calibration bias can persist through repeats.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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