Solutions to AP PHYSICS – SUMMER PROBLEM SET
MEASUREMENT
1.) The only SI standard represented by an artifact is the (a) meter, (b) kilogram, (c)
second, or (d) electric charge.
Answer: (b)
2.) Which of the following is not an SI base unit? (a) length, (b) mass, (c) weight, or (d)
time.
Answer: (c)
3.) Which one of the following is the SI unit of mass? (a) pound, (b) gram, (c) kilogram,
or (d) ton.
Answer: (c)
4.) Can dimensional analysis tell you whether you have used the correct equation in
solving a problem? Explain.
Answer: No. Dimensional analysis can only show if quantities involved follow correct
relationship. It does not show if it is physically possible or numerically correct.
5.) If x refers to distance, v0 and v to speeds, a to acceleration, and t to time, which of the
following equations is dimensionally correct?
(a) x = v0t + at3, (b) v2 = v02 + 2at, (c) x = at + vt2, or (d) v2 = v02 + 2ax.
Answer: (d)
6.) Is the equation v = v0 sin  – gt2 dimensionally correct? Use SI unit analysis to find
out. (v and v0 are velocities,  is an angle, t is time, and g is acceleration.) 
Answer: No.
Left of the equation has dimension of velocity, which is [L]/[T]. However, the term gt2 has
the dimension of [L]/[T]2x[T]2=[L]. So the equation is not dimensionally correct.
7.) Newton’s second law of motion is expressed by the equation F = ma, where F
represents force, m is mass, and a is acceleration. (a) The SI unit of force is,
appropriately, called the Newton (N). What are the units of the Newton in terms of base
quantities? (b) An equation for force associated with uniform circular motion is F = mv2 /
r, where v is speed and r is the radius of the circular path. Does this equation give the
same units for the Newton?
Answer: (a) Since F = ma, the unit for Force will be kg m/s2.
(b) Yes. Since unit of mv2 / r is kg(m/s)2/m, i.e. kg m/s2. It is the same as Newton as shown
in (a).
8.) Standing at 452 m, the Petronas Twin Towers in Malaysia is one of the tallest
buildings in the world. What is its height in feet?
Answer: 452 m = 452 m x 3.28ft/m = 1483 ft.
Solutions to AP PHYSICS – SUMMER PROBLEM SET
9.) If blood flows with an average speed of 0.35 m/s in the human circulatory system,
how many miles does a blood cell travel in 1 h?
Answer: distance = 0.35 m/s x 3600 s = 1260 m = 1260 meters x 0.0006213 miles/meter
= 0.78 miles.
10.) The density of metal mercury is 13.6 g/cm3. (a) What is this density as expressed in
kg/m3? (b) How many kilograms of mercury would be required to fill a 0.250-L
container?
Answer: (a) density = 13.6 g/cm3 = 13.6 x 10-3 kg/(10-2)3m3=13.6 x 103 kg/ m3.
(b) mass = density x volume = 13.6 g/cm3x 0.250 L = 13.6 g/cm3x0.250 x 1000 cm3
=3400 g = 3.4 kg.
11.) Which of the following has the greatest number of significant figures? (a) 103.07, (b)
124.5, (c) 0.09916, or (d) 5.408 x 105.
Answer: (a) 5 sig. (b) 4 sig. (c) 4 sig. (d) 3 sig.
12.) In a multiplication and/or division operation involving the numbers
15437, 201.08, and 408.0 x 105, the result should be rounded to how many significant
figures? (a) 3, (b) 4, (c) 5, or (d) any number.
Answer: (b)
13.) If a measured length is reported as 25.483 cm, could this length have been measured
with an ordinary meter-stick whose smallest division is millimeters? Discuss in terms of
significant figures.
Answer: No. Since an ordinary meterstick’s smallest division is millimeter. Millimeter
will be the smallest unit one can measure with certainty. The estimated number will be a
fraction of a millimeter. 25.483 cm = 254.83 mm. It has 5 significant numbers when it
can only be measured accurately with 4 significant numbers.
14.) A compact disc (CD) has a diameter of approximately 12 cm. What is its area in m2?
Answer: area = D/2)2=3.14 x (0.06) 2 m2=0.011 m2
15.) In doing a problem, a student adds 46.9 m and 5.72 m and then subtracts 38 m from
the result. (a) How many decimal places will the final answer have, (1) zero, (2) one, or
(3) two? (b) What is the final answer?
Answer: (a) 1; (b) ans=46.9+5.72-38=47+6-38=15 m