Measurement & Scientific Notation
accuracy
How close a measured value is to the true or accepted value.
Convert 1750 m to ft.
1 ft
1750 m × ────────── = 5741.47 ft
0.3048 m
Final: 5.74 × 10³ ft
Motion in which velocity remains unchanged; equal distances are traveled during equal time intervals.
constant velocity
The rate at which velocity changes with time.
acceleration
Explain retrograde motion and compare how Ptolemy and Copernicus accounted for it.
Retrograde motion is apparent temporary backward motion against the stars. Ptolemy explained it with epicycles; Copernicus explained it by relative orbital motion, such as Earth overtaking another planet.
precision
The fineness or resolution of a measurement; how finely an instrument measures.
Convert 32.16 ft/s² to m/s².
32.16 ft 0.3048 m
────────── × ────────── = 9.802 m/s²
s² 1 ft
The rate at which position or distance changes with time in the one-dimensional treatment of this chapter.
velocity
Motion in which velocity changes by the same amount during equal time intervals.
uniform acceleration
State Kepler’s First Law of Planetary Motion.
Kepler’s First Law: each planetary orbit is an ellipse, with the Sun at one focus.
meniscus
The curved surface of a liquid inside a narrow container.
Convert 65 mi/hr to m/s.
65 mi 1609 m 1 hr
─────── × ──────── × ──────── = 29 m/s
1 hr 1 mi 3600 s
A train travels 25.1 miles in 0.50 hr. Calculate the velocity of the train. Give the answer in mi/hr and m/s.
25.1 mi
v = ───────── = 50.2 mi/hr
0.50 hr
Convert to m/s:
50.2 mi 1609 m 1 hr
──────── × ─────── × ─────── = 22.4 m/s,
1 hr 1 mi 3600 s
which the text rounds to 22 m/s.
About 9.8 m/s² downward when air resistance is ignored.
gravitational acceleration near Earth
List three observations made by Galileo and explain what they challenged.
Galileo observed the Moon’s irregular surface, sunspots, and moons orbiting Jupiter. These challenged perfect heavens, unchanging heavens, and the assumption that everything orbits Earth.
How many significant digits are in 0.00420? Explain briefly.
0.00420 has 3 significant digits: 4, 2, and the final 0 after the decimal.
Convert 5.65 × 10² mm² to in²
1 cm 1 cm
5.65 × 10² mm² × ─────── × ─────── = 5.65 cm²
10 mm 10 mm
1 in 1 in
5.65 cm² × ───────── × ───────── = 0.876 in²
2.54 cm 2.54 cm
How far can you walk in 4.25 hr if you keep a steady pace of 5.0000 km/hr? State your answer in km.
5.0000 km
───────── × 4.25 hr = 21.25 km, rounded to
1 hr
21.3 km.
A car starts from rest and accelerates to 45 mi/hr in 36 s. Calculate the acceleration in m/s².
a ≈ 0.56 m/s²
Why should the Galileo controversy not be reduced to the simple slogan “science versus religion”?
A good answer should mention scientific evidence, competing models, biblical interpretation, authority/procedure, and the danger of oversimplifying history.
Write 5740 in scientific notation using three significant digits.
5740 = 5.74 × 103
Convert 750 cm³ to m³.
1 L 1 m³
750 cm³ × ────────── × ──────── = 0.00075 m³
1000 cm³ 1000 L
= 7.5 × 10⁻⁴ m³
An object travels 3.0 km at constant velocity in 1 hr 20.0 min. Calculate the object’s velocity in m/s.
1 hr 20.0 min = 80.0 min = 4800 s. 3.0 km = 3000 m.
3000 m
v = ───────── = 0.625 m/s, rounded to 0.63 m/s.
4800 s
If an object starts at 0 m/s and accelerates downward at 9.8 m/s², what is its velocity after 1 s, 2 s, 3 s, and 4 s?
After 1 s: 9.8 m/s downward. After 2 s: 19.6 m/s downward. After 3 s: 29.4 m/s downward. After 4 s: 39.2 m/s downward.
Explain Augustine’s warning in your own words.
Augustine’s warning: Christians should not carelessly attach Scripture’s authority to our own scientific or interpretive mistakes; Scripture is authoritative, but our interpretations must be humble.