qu.1.topic=Ch 1, Sec 1 - Units of Mass, Time, and Length@ qu.1.1.mode=Multiple Choice@ qu.1.1.editing=useHTML@ qu.1.1.name=Length@ qu.1.1.question=Which of the following is a unit of length?@ qu.1.1.answer=1@ qu.1.1.choice.1=meter (m)@ qu.1.1.choice.2=kilogram (kg)@ qu.1.1.choice.3=second (s)@ qu.1.1.choice.4=Ampere (A)@ qu.1.1.choice.5=Kelvin (K)@ qu.1.2.mode=Multiple Choice@ qu.1.2.editing=useHTML@ qu.1.2.name=Mass@ qu.1.2.question=Which of the following is a unit of mass?@ qu.1.2.answer=2@ qu.1.2.choice.1=meter (m)@ qu.1.2.choice.2=kilogram (kg)@ qu.1.2.choice.3=second (s)@ qu.1.2.choice.4=Ampere (A)@ qu.1.2.choice.5=Kelvin (K)@ qu.1.3.mode=Multiple Choice@ qu.1.3.editing=useHTML@ qu.1.3.name=Time@ qu.1.3.question=Which of the following is a unit of time?@ qu.1.3.answer=3@ qu.1.3.choice.1=meter (m)@ qu.1.3.choice.2=kilogram (kg)@ qu.1.3.choice.3=second (s)@ qu.1.3.choice.4=Ampere (A)@ qu.1.3.choice.5=Kelvin (K)@ qu.1.4.mode=Multiple Choice@ qu.1.4.editing=useHTML@ qu.1.4.name=Meter@ qu.1.4.question=The meter is a unit used to measure:@ qu.1.4.answer=1@ qu.1.4.choice.1=length@ qu.1.4.choice.2=mass@ qu.1.4.choice.3=time@ qu.1.4.choice.4=electric current@ qu.1.4.choice.5=temperature@ qu.1.5.mode=Multiple Choice@ qu.1.5.editing=useHTML@ qu.1.5.name=Kilogram@ qu.1.5.question=The kilogram is a unit used to measure:@ qu.1.5.answer=2@ qu.1.5.choice.1=length@ qu.1.5.choice.2=mass@ qu.1.5.choice.3=time@ qu.1.5.choice.4=electric current@ qu.1.5.choice.5=temperature@ qu.1.6.mode=Multiple Choice@ qu.1.6.editing=useHTML@ qu.1.6.name=Second@ qu.1.6.question=The second is a unit used to measure:@ qu.1.6.answer=3@ qu.1.6.choice.1=length@ qu.1.6.choice.2=mass@ qu.1.6.choice.3=time@ qu.1.6.choice.4=electric current@ qu.1.6.choice.5=temperature@ qu.1.7.mode=Multiple Selection@ qu.1.7.editing=useHTML@ qu.1.7.name=Units of Length@ qu.1.7.question=Which of the following units are used to measure length (choose three)?@ qu.1.7.answer=1,3,4@ qu.1.7.choice.1=meter (m)@ qu.1.7.choice.2=second (s)@ qu.1.7.choice.3=terameter (Tm)@ qu.1.7.choice.4=millimeter (mm)@ qu.1.7.choice.5=gram (g)@ qu.1.7.choice.6=milligram (mg)@ qu.1.8.mode=Multiple Selection@ qu.1.8.editing=useHTML@ qu.1.8.name=Units of Time@ qu.1.8.question=Which of the following units are used to measure time (choose two)?@ qu.1.8.answer=1,2@ qu.1.8.choice.1=nanosecond (ns)@ qu.1.8.choice.2=gigasecond (Gs)@ qu.1.8.choice.3=kilometer (km)@ qu.1.8.choice.4=kilogram (kg)@ qu.1.8.choice.5=Kelvin (K)@ qu.1.9.mode=Multiple Selection@ qu.1.9.editing=useHTML@ qu.1.9.name=Units of Mass@ qu.1.9.question=Which of the following units are used to measure mass (choose three)?@ qu.1.9.answer=1,5,6@ qu.1.9.choice.1=kilogram (kg)@ qu.1.9.choice.2=second (s)@ qu.1.9.choice.3=terameter (Tm)@ qu.1.9.choice.4=millimeter (mm)@ qu.1.9.choice.5=gram (g)@ qu.1.9.choice.6=milligram (mg)@ qu.2.topic=Ch 1, Sec 2 - Scientific Notation@ qu.2.1.mode=Multiple Choice@ qu.2.1.editing=useHTML@ qu.2.1.name=123,000@ qu.2.1.question=In scientific notation, the number 123,000 would be written as:@ qu.2.1.answer=3@ qu.2.1.choice.1=123 x 10²@ qu.2.1.choice.2=12.3 x 10⁴@ qu.2.1.choice.3=1.23 x 10⁵@ qu.2.1.choice.4=1.23 x 10⁶@ qu.2.1.choice.5=1.23 x 10⁷@ qu.2.1.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.1.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.2.mode=Multiple Choice@ qu.2.2.editing=useHTML@ qu.2.2.name=2,300,000@ qu.2.2.question=In scientific notation, the number 2,300,000 would be written as:@ qu.2.2.answer=4@ qu.2.2.choice.1=2.3 x 10³@ qu.2.2.choice.2=230 x 10⁴@ qu.2.2.choice.3=23 x 10⁵@ qu.2.2.choice.4=2.3 x 10⁶@ qu.2.2.choice.5=2.3 x 10⁷@ qu.2.2.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.2.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.3.mode=Multiple Choice@ qu.2.3.editing=useHTML@ qu.2.3.name=37,000@ qu.2.3.question=In scientific notation, the number 37,000 would be written as:@ qu.2.3.answer=2@ qu.2.3.choice.1=37 x 10³@ qu.2.3.choice.2=3.7 x 10⁴@ qu.2.3.choice.3=0.37 x 10⁵@ qu.2.3.choice.4=0.37 x 10⁶@ qu.2.3.choice.5=3.7 x 10⁷@ qu.2.3.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.3.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.4.mode=Multiple Choice@ qu.2.4.editing=useHTML@ qu.2.4.name=7,420@ qu.2.4.question=In scientific notation, the number 7,420 would be written as:@ qu.2.4.answer=1@ qu.2.4.choice.1=7.42 x 10³@ qu.2.4.choice.2=0.742 x 10⁴@ qu.2.4.choice.3=0.0742 x 10⁵@ qu.2.4.choice.4=7.42 x 10⁶@ qu.2.4.choice.5=742 x 10⁷@ qu.2.4.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.4.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.5.mode=Multiple Choice@ qu.2.5.editing=useHTML@ qu.2.5.name=11,900,000@ qu.2.5.question=In scientific notation, the number 11,900,000 would be written as:@ qu.2.5.answer=5@ qu.2.5.choice.1=1.19 x 10³@ qu.2.5.choice.2=1.19 x 10⁴@ qu.2.5.choice.3=119 x 10⁵@ qu.2.5.choice.4=11.9 x 10⁶@ qu.2.5.choice.5=1.19 x 10⁷@ qu.2.5.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.5.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.6.mode=Multiple Choice@ qu.2.6.editing=useHTML@ qu.2.6.name=0.0041@ qu.2.6.question=In scientific notation, the number 0.0041 would be written as:@ qu.2.6.answer=1@ qu.2.6.choice.1=4.1 x 10^-3@ qu.2.6.choice.2=41 x 10^-4@ qu.2.6.choice.3=410 x 10^-5@ qu.2.6.choice.4=4.1 x 10^-6@ qu.2.6.choice.5=4.1 x 10^-7@ qu.2.6.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.6.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.7.mode=Multiple Choice@ qu.2.7.editing=useHTML@ qu.2.7.name=0.0000057@ qu.2.7.question=In scientific notation, the number 0.0000057 would be written as:@ qu.2.7.answer=4@ qu.2.7.choice.1=5.7 x 10^-3@ qu.2.7.choice.2=570 x 10^-8@ qu.2.7.choice.3=5.7 x 10^-5@ qu.2.7.choice.4=5.7 x 10^-6@ qu.2.7.choice.5=57 x 10^-7@ qu.2.7.hint.1=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.7.comment=Scientific notation is a mathematical shorthand. It is represented by a base (a number that has a single nonzero digit to the left of the decimal), which is multiplied by a power of 10.@ qu.2.8.mode=Multiple Choice@ qu.2.8.editing=useHTML@ qu.2.8.name=1.8 x 10²@ qu.2.8.question=Written in scientific notation, 1.8 x 10² represents the number:@ qu.2.8.answer=1@ qu.2.8.choice.1=180@ qu.2.8.choice.2=1,800@ qu.2.8.choice.3=18,000@ qu.2.8.choice.4=180,000@ qu.2.8.choice.5=1,800,000@ qu.2.9.mode=Multiple Choice@ qu.2.9.editing=useHTML@ qu.2.9.name=5.6 x 10⁸@ qu.2.9.question=Written in scientific notation, 5.6 x 10⁸ represents the number:@ qu.2.9.answer=4@ qu.2.9.choice.1=5,600@ qu.2.9.choice.2=56,000@ qu.2.9.choice.3=560,000@ qu.2.9.choice.4=560,000,000@ qu.2.9.choice.5=5,600,000,000@ qu.2.10.mode=Multiple Choice@ qu.2.10.editing=useHTML@ qu.2.10.name=2.37 x 10²@ qu.2.10.question=Written in scientific notation, 2.37 x 10² represents the number:@ qu.2.10.answer=2@ qu.2.10.choice.1=23.7@ qu.2.10.choice.2=237@ qu.2.10.choice.3=2,370@ qu.2.10.choice.4=23,700@ qu.2.10.choice.5=23,700,000@ qu.3.topic=Ch 1, Sec 3 - Metric Prefixes@ qu.3.1.mode=Multiple Choice@ qu.3.1.editing=useHTML@ qu.3.1.name=centi - common@ qu.3.1.question=The metric prefix centi means:@ qu.3.1.answer=3@ qu.3.1.choice.1=10¹@ qu.3.1.choice.2=10^-1@ qu.3.1.choice.3=10^-2@ qu.3.1.choice.4=10^-3@ qu.3.1.choice.5=10^-4@ qu.3.2.mode=Multiple Choice@ qu.3.2.editing=useHTML@ qu.3.2.name=kilo - common@ qu.3.2.question=The metric prefix kilo means:@ qu.3.2.answer=4@ qu.3.2.choice.1=10^-1@ qu.3.2.choice.2=10¹@ qu.3.2.choice.3=10²@ qu.3.2.choice.4=10³@ qu.3.2.choice.5=10⁴@ qu.3.3.mode=Multiple Choice@ qu.3.3.editing=useHTML@ qu.3.3.name=milli - common@ qu.3.3.question=The metric prefix milli means:@ qu.3.3.answer=2@ qu.3.3.choice.1=10^-2@ qu.3.3.choice.2=10^-3@ qu.3.3.choice.3=10^-4@ qu.3.3.choice.4=10^-5@ qu.3.3.choice.5=10^-6@ qu.3.4.mode=Multiple Choice@ qu.3.4.editing=useHTML@ qu.3.4.name=micro - common@ qu.3.4.question=The metric prefix micro means:@ qu.3.4.answer=5@ qu.3.4.choice.1=10^-2@ qu.3.4.choice.2=10^-3@ qu.3.4.choice.3=10^-4@ qu.3.4.choice.4=10^-5@ qu.3.4.choice.5=10^-6@ qu.3.5.mode=Multiple Choice@ qu.3.5.editing=useHTML@ qu.3.5.name=mega - common@ qu.3.5.question=The metric prefix mega means:@ qu.3.5.answer=5@ qu.3.5.choice.1=10²@ qu.3.5.choice.2=10³@ qu.3.5.choice.3=10⁴@ qu.3.5.choice.4=10⁵@ qu.3.5.choice.5=10⁶@ qu.3.6.mode=Multiple Choice@ qu.3.6.editing=useHTML@ qu.3.6.name=giga - common@ qu.3.6.question=The metric prefix giga means:@ qu.3.6.answer=4@ qu.3.6.choice.1=10⁶@ qu.3.6.choice.2=10⁷@ qu.3.6.choice.3=10⁸@ qu.3.6.choice.4=10⁹@ qu.3.6.choice.5=10¹⁰@ qu.3.7.mode=Multiple Choice@ qu.3.7.editing=useHTML@ qu.3.7.name=peta - uncommon@ qu.3.7.question=The metric prefix peta means:@ qu.3.7.answer=5@ qu.3.7.choice.1=10²@ qu.3.7.choice.2=10³@ qu.3.7.choice.3=10⁴@ qu.3.7.choice.4=10⁵@ qu.3.7.choice.5=none of these@ qu.3.8.mode=Multiple Choice@ qu.3.8.editing=useHTML@ qu.3.8.name=deka - uncommon@ qu.3.8.question=The metric prefix deka means:@ qu.3.8.answer=3@ qu.3.8.choice.1=10³@ qu.3.8.choice.2=10²@ qu.3.8.choice.3=10¹@ qu.3.8.choice.4=10^-1@ qu.3.8.choice.5=10^-2@ qu.3.9.mode=Multiple Choice@ qu.3.9.editing=useHTML@ qu.3.9.name=tera - uncommon@ qu.3.9.question=The metric prefix tera means:@ qu.3.9.answer=2@ qu.3.9.choice.1=10¹¹@ qu.3.9.choice.2=10¹²@ qu.3.9.choice.3=10¹³@ qu.3.9.choice.4=10¹⁴@ qu.3.9.choice.5=10¹⁵@ qu.3.10.mode=Multiple Choice@ qu.3.10.editing=useHTML@ qu.3.10.name=hecto - uncommon@ qu.3.10.question=The metric prefix hecto means:@ qu.3.10.answer=1@ qu.3.10.choice.1=10²@ qu.3.10.choice.2=10³@ qu.3.10.choice.3=10⁴@ qu.3.10.choice.4=10⁵@ qu.3.10.choice.5=10⁶@ qu.3.11.mode=Multiple Choice@ qu.3.11.editing=useHTML@ qu.3.11.name=pico - uncommon@ qu.3.11.question=The metric prefix pico means:@ qu.3.11.answer=1@ qu.3.11.choice.1=10^-12@ qu.3.11.choice.2=10^-13@ qu.3.11.choice.3=10^-14@ qu.3.11.choice.4=10^-15@ qu.3.11.choice.5=10^-16@ qu.3.12.mode=Multiple Selection@ qu.3.12.editing=useHTML@ qu.3.12.name=> 1000 - Applications@ qu.3.12.question=Which of the following prefixes are greater than 1000 (choose three)?@ qu.3.12.answer=1,2,6@ qu.3.12.choice.1=peta (P)@ qu.3.12.choice.2=giga (G)@ qu.3.12.choice.3=milli (m)@ qu.3.12.choice.4=micro (m)@ qu.3.12.choice.5=centi (c)@ qu.3.12.choice.6=mega (M)@ qu.3.13.mode=Multiple Selection@ qu.3.13.editing=useHTML@ qu.3.13.name=< 1 - Applications@ qu.3.13.question=Which of the following prefixes are less than 1 (choose two)?@ qu.3.13.answer=2,4@ qu.3.13.choice.1=hecto (h)@ qu.3.13.choice.2=femto (f)@ qu.3.13.choice.3=mega (m)@ qu.3.13.choice.4=deci (d)@ qu.3.13.choice.5=deka (da)@ qu.3.13.choice.6=kilo (k)@ qu.3.14.mode=Multiple Selection@ qu.3.14.editing=useHTML@ qu.3.14.name=1 Mm - Applications@ qu.3.14.question=Which of the following quantities give 1 megameter (Mm) if multiplied or divided by 10³ (choose two)?@ qu.3.14.answer=1,3@ qu.3.14.choice.1=1 gigameter (Gm)@ qu.3.14.choice.2=1 terameter (Tm)@ qu.3.14.choice.3=1 kilometer (km)@ qu.3.14.choice.4=1 nanometer (nm)@ qu.3.14.choice.5=1 decimeter (dm)@ qu.3.15.mode=Multiple Selection@ qu.3.15.editing=useHTML@ qu.3.15.name=Larger Number@ qu.3.15.question=Which of the following prefixes become a $larger number when $squared? (Choose three).@ qu.3.15.answer=$ans@ qu.3.15.random= $integer\=rint(2); $squared\=switch(rint(2),"squared","cubed"); $larger\=switch($integer,"larger","smaller"); $ans\=switch($integer,"1,2,3","4,5,6")@ qu.3.15.choice.1=deka (da)@ qu.3.15.choice.2=kilo (k)@ qu.3.15.choice.3=tera (T)@ qu.3.15.choice.4=femto (f)@ qu.3.15.choice.5=micro (m)@ qu.3.15.choice.6=deci (d)@ qu.4.topic=Ch 1, Sec 4 - Analysis of Dimensions@ qu.4.1.mode=Randomized Formula@ qu.4.1.editing=useHTML@ qu.4.1.name=2ax=v² - v_o²@ qu.4.1.question=What are the dimensions of the $left side of the equation 2ax = v² - v_o², where a is acceleration (measured in m/s²), x is position (measured in m), and v is velocity (measured in m/s)?@ qu.4.1.answer=m^2/s^2@ qu.4.1.random=$left\=switch(rint(2),"left","right")@ qu.4.2.mode=Randomized Formula@ qu.4.2.editing=useHTML@ qu.4.2.name=v(t)=t(p)^1/3 @ qu.4.2.question=Velocity (measured in m/s) as a function of time is expressed by the following function:

,
where t is time (in seconds, s). Find the dimensions of p.@ qu.4.2.answer=m^3/s^6@ qu.4.2.hint.1=Let us suppose the units of p to be [z]. Substitute this and the units of other quantities in the original equation.@ qu.4.2.hint.2=In terms of units, the original equation is written as follows:

@ qu.4.2.comment= 1. Let us suppose the units of p to be [z]. Substitute this and the units of other quantities in the original equation.

2. In terms of units, the original equation is written as follows:

3. Solving this equation for [z], we obtain the units of p:

@ qu.4.3.mode=Randomized Formula@ qu.4.3.editing=useHTML@ qu.4.3.name=a=pi*x@ qu.4.3.question=Acceleration (measured in m/s²) is related to time (measured in seconds, s) and distance (measured in meters, m) by the following formula:

.
Find the value of n that makes this equation dimensionally consistent.@ qu.4.3.answer=8@ qu.4.3.hint.1= Substituting the units of all quantities in the given equation, we obtain:

Note that p has no units. @ qu.4.3.comment= Substituting the units of all quantities in the given equation, we obtain:

Note that p has no units.
In order for this equation to be true, the powers of respective units of measurement must be equal, so to find n, we need to solve 2 = n/4, which gives n = 8. @ qu.4.4.mode=Randomized Formula@ qu.4.4.editing=useHTML@ qu.4.4.name=f of m on a spring@ qu.4.4.question=The frequency (measured in 1/s) of oscillation of a mass on a spring is given by

,
where m is the mass (measured in kg). Find the dimensions that the constant k must have in order for this equation to be dimensionally accurate. (Give your answer in basic SI units.)@ qu.4.4.answer=kg/s^2@ qu.4.4.hint.1=Let us suppose the units of k to be [z]. Substitute this and the units of other quantities in the original equation.@ qu.4.4.hint.2=In terms of units, the original equation is written as follows:

Note that p is dimensionless (has no units).@ qu.4.4.comment= 1.Let us suppose the units of k to be [z]. Substitute this and the units of other quantities in the original equation.

2. In terms of units, the original equation is written as follows:

Note that p is dimensionless (has no units).

3. Solving this equation for [z], we obtain that the units of k are kg/s².@ qu.4.5.mode=Randomized Formula@ qu.4.5.editing=useHTML@ qu.4.5.name=v=v_ot+a/t@ qu.4.5.question=The velocity (measured in m/s) of a particle is described by the following formula:
,
where t is time (in seconds, s) and a is acceleration (measured in m/s²). What dimensions must k have in order for that equation to be dimensionally correct?@ qu.4.5.answer=s^2@ qu.4.5.hint.1=Rewrite the given equation in terms of dimensions of the quantities using [k] to represent the dimensions of k.@ qu.4.5.hint.2=In terms of units the equation becomes:

Because solving for either [k] will give the same result, we can use either of the terms on the right side of the equation. Let us choose the second term and ignore the first one. Thus the equation becomes:

Solving this equation for [k] will give the final answer.@ qu.4.5.comment= 1. Rewrite the given equation in terms of dimensions of the quantities using [k] to represent the dimensions of k.

2. In terms of units the equation becomes:

Solving this equation for [k] will give the final answer.

3. [k] = s².@ qu.4.6.mode=Randomized Formula@ qu.4.6.editing=useHTML@ qu.4.6.name=x=at²e^bv@ qu.4.6.question=Position (measured in meters, m) is related to time t (measured in seconds, s), acceleration a (measured in m/s²), and instantaneous velocity v (measured in m/s) according to the formula x = at²e^bv (where e^bv is an exponential function). Find the dimensions of b so that the equation is dimensionally consistent.@ qu.4.6.answer=s/m@ qu.4.6.hint.1=Rewrite the given equation in terms of dimensions of the quantities using [b] to represent the dimensions of b.@ qu.4.6.hint.2=In terms of units the equation becomes:

@ qu.4.6.hint.3=Because exponents are dimensionless, the units in the exponent must cancel.@ qu.4.6.comment= 1. Rewrite the given equation in terms of dimensions of the quantities using [b] to represent the dimensions of b.

2. In terms of units the equation becomes:

3. Because exponents are dimensionless, the units in the exponent must cancel.

4. In order to cancel the units of velocity (m/s), the units of b must be s/m.@ qu.4.7.mode=Randomized Formula@ qu.4.7.editing=useHTML@ qu.4.7.name=t=zv²/a⁴@ qu.4.7.question=A time interval in an experiment can be calculated using the formula
,
where v is velocity (measured in m/s), a is acceleration (measured in m/s²), and t is measured in seconds, s. Find the dimensions of the constant z that would keep the equation dimensionally correct.@ qu.4.7.hint.1=Rewrite the given equation in terms of the dimensions of the quantities. Replace z with [z] to indicate the respective dimensions of the quantity z.@ qu.4.7.hint.2=In terms of units, the given equation becomes
.
Now we need to solve for [z].@ qu.4.7.hint.3=Solving for [z], we get:
@ qu.4.7.answer=m^2/s^5@ qu.4.7.comment=1. Rewrite the given equation in terms of the dimensions of the quantities. Replace z with [z] to indicate the respective dimensions of the quantity z.

2. In terms of units, the given equation becomes
.
Now we need to solve for [z].

3. Solving for [z], we get:
@ qu.4.8.mode=Randomized Formula@ qu.4.8.editing=useHTML@ qu.4.8.name=v_o²=v²-2x/k@ qu.4.8.question=What dimensions must the constant k have in order for the equation

to be dimensionally correct? (Note that v is velocity measured in m/s, x is position measured in meters, m).@ qu.4.8.answer=s^2/m@ qu.4.8.hint.1=Rewrite the equation in terms of dimensions of the quantities. Use [k] to represent the dimensions of k.@ qu.4.8.hint.2=In terms of units, the equation becomes:

In order to subtract the terms on the right side of the equation they must be dimensionally consistent. Note that the numerical constant can be ignored.@ qu.4.8.comment= 1. Rewrite the equation in terms of dimensions of the quantities. Use [k] to represent the dimensions of k.

2. In terms of units, the equation becomes:

@ qu.5.topic=Ch 1, Sec 5 - Significant Figures@ qu.5.1.mode=Randomized Formula@ qu.5.1.editing=useHTML@ qu.5.1.name=0.004@ qu.5.1.question=How many significant figures does the number $num1 contain?@ qu.5.1.answer=$ans@ qu.5.1.random= $integer\=rint(5); $num\=switch($integer, 0.004, 0.004, 0.004, 0.004, 0.004); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.2.mode=Randomized Formula@ qu.5.2.editing=useHTML@ qu.5.2.name=0.06@ qu.5.2.question=How many significant figures does the number $num1 contain?@ qu.5.2.answer=$ans@ qu.5.2.random= $integer\=rint(5); $num\=switch($integer, 0.06, 0.06, 0.06, 0.06, 0.06); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.3.mode=Randomized Formula@ qu.5.3.editing=useHTML@ qu.5.3.name=36.005@ qu.5.3.question=How many significant figures does the number $num1 contain?@ qu.5.3.answer=$ans@ qu.5.3.random= $integer\=rint(5); $num\=switch($integer, 36.005, 36.005, 36.005, 36.005, 36.005); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.4.mode=Randomized Formula@ qu.5.4.editing=useHTML@ qu.5.4.name=7.004@ qu.5.4.question=How many significant figures does the number $num1 contain?@ qu.5.4.answer=$ans@ qu.5.4.random= $integer\=rint(5); $num\=switch($integer, 7.004, 7.004, 7.004, 7.004, 7.004); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.5.mode=Randomized Formula@ qu.5.5.editing=useHTML@ qu.5.5.name=14@ qu.5.5.question=How many significant figures does the number $num1 contain?@ qu.5.5.answer=$ans@ qu.5.5.random= $integer\=rint(5); $num\=switch($integer, 14, 14, 14, 14, 14); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.6.mode=Randomized Formula@ qu.5.6.editing=useHTML@ qu.5.6.name=2.4 x 10⁴@ qu.5.6.question=How many significant figures does the number $num1 x 10⁴ contain?@ qu.5.6.answer=$ans@ qu.5.6.random= $integer\=rint(5); $num\=switch($integer, 2.4, 2.4, 2.4, 2.4, 2.4); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.7.mode=Randomized Formula@ qu.5.7.editing=useHTML@ qu.5.7.name=534@ qu.5.7.question=How many significant figures does the number $num1 x 10⁴ contain?@ qu.5.7.answer=$ans@ qu.5.7.random= $integer\=rint(5); $num\=switch($integer, 534, 534, 534, 534, 534); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.8.mode=Randomized Formula@ qu.5.8.editing=useHTML@ qu.5.8.name=6.22 x 10²@ qu.5.8.question=How many significant figures does the number $num1 x 10² contain?@ qu.5.8.answer=$ans@ qu.5.8.random= $integer\=rint(5); $num\=switch($integer, 6.22, 6.22, 6.22, 6.22, 6.22); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.5.9.mode=Randomized Formula@ qu.5.9.editing=useHTML@ qu.5.9.name=7.421 x 10⁶@ qu.5.9.question=How many significant figures does the number $num1 x 10² contain?@ qu.5.9.answer=$ans@ qu.5.9.random= $integer\=rint(5); $num\=switch($integer, 7.421, 7.421, 7.421, 7.421, 7.421); $num1\=sig($integer+1,$num); $ans\=sig(1,$integer+1);@ qu.6.topic=Ch 1, Sec 6 - Unit Conversions@ qu.6.1.mode=Randomized Formula@ qu.6.1.editing=useHTML@ qu.6.1.name=Period of Life of a Human@ qu.6.1.question=Suppose that the average period of life of a human being is $lifeperiod years. Express this amount of time in seconds. (Suppose 1 year to be 365 days). Use 3 significant figures.@ qu.6.1.answer=$ans s(1 ? 0.05)@ qu.6.1.random= $lifeperiod\=rand(64,69,3); $ans\=sig(3,3.1536*10^7*$lifeperiod);@ qu.6.2.mode=Randomized Formula@ qu.6.2.editing=useHTML@ qu.6.2.name=Express the speed of light@ qu.6.2.question=The speed of light is equal 3.00 x 10⁸ m/s. Express this speed in $units. Use 3 significant figures.@ qu.6.2.answer=$ans $units1(1 ? 0.025)@ qu.6.2.random= $integer\=rint(2); $units\=switch($integer, "meters per kilosecond, m/ks", "nanometers per second, nm/s"); $units1\=switch($integer, "m/ks", "nm/s"); $calculation\=switch($integer, 3*10^11, 3*10^17); $ans\=sig(3,$calculation)@ qu.6.3.mode=Randomized Formula@ qu.6.3.editing=useHTML@ qu.6.3.name=Acceleration - Space Ship@ qu.6.3.question=The acceleration of a space ship is equal to $a·g, where g is acceleration due to gravity and is equal to 9.81 m/s². Express a in $units.@ qu.6.3.answer=$ans $units1(1 ? 0.05)@ qu.6.3.random= $a\=rand(3,4.9,3); $integer\=rint(3); $units\=switch($integer, "km/s²", "km/h²", "m/h²"); $units1\=switch($integer, "km/s^2", "km/h^2", "m/h^2"); $calculation\=switch($integer, $a*9.81/10^3, $a*9.81*60^4/10^3, $a*9.81*60^4); $ans\=sig(3,$calculation)@ qu.6.3.hint.1=When converting between squared units, the conversion factor used must also be squared.@ qu.6.3.comment=When converting between squared units, the conversion factor used must also be squared.@ qu.6.4.mode=Randomized Formula@ qu.6.4.editing=useHTML@ qu.6.4.name=Cube - Volume@ qu.6.4.question=A surface area of a side of the cube is equal to $s m². What is its volume expressed in $units?@ qu.6.4.answer=$ans $units1(1 ? 0.05)@ qu.6.4.random= $s\=rand(10,50,3); $integer\=rint(2); $units\=switch($integer, "liters, l", "cm³"); $units1\=switch($integer, "l", "cm^3"); $calculation\=switch($integer, ($s^(3/2))*1000, ($s^(3/2))*10^6); $ans\=sig(3,$calculation)@ qu.6.4.hint.1=The volume of a cube is equal to its side cubed: V = s³. Solve for the length of the side of the cube first.@ qu.6.4.hint.2=When converting between cubed units, the conversion factor must also be cubed.@ qu.6.4.comment= 1. The volume of a cube is equal to its side cubed: V = s³. Solve for the length of the side of the cube first.

2. When converting between cubed units, the conversion factor must also be cubed.@ qu.6.5.mode=Randomized Formula@ qu.6.5.editing=useHTML@ qu.6.5.name=Distance - Light@ qu.6.5.question=The $dname is $value m. How many hours, h, will it take a ray of light to travel that distance?@ qu.6.5.answer=$ans h(1 ? 0.05)@ qu.6.5.random= $integer\=rint(5); $dname\=switch($integer, "diameter of our galaxy", "distance from the Earth to the nearest large galaxy", "distance from the Earth to the nearest star", "distance from the Earth to the Sun", "radius of the Earth"); $value\=switch($integer, "8.00 x 10²⁰", "2.00 x 10²²", "4.00 x 10¹⁶", "1.50 x 10¹¹", "6.37 x 10⁶"); $calculation\=switch($integer, 7.41E8, 1.85E10, 37037, 0.139, 5.8981*10^(-6)); $ans\=sig(3,$calculation)@ qu.6.6.mode=Multiple Choice@ qu.6.6.editing=useHTML@ qu.6.6.name=Speed Limit@ qu.6.6.question=The speed limit on many highways is 65 mi/h. What is this speed limit written in ft/s (feet per second)?@ qu.6.6.answer=3@ qu.6.6.choice.1=75@ qu.6.6.choice.2=85@ qu.6.6.choice.3=95@ qu.6.6.choice.4=105@ qu.6.6.choice.5=115@ qu.6.6.choice.6=125@ qu.6.7.mode=Multiple Choice@ qu.6.7.editing=useHTML@ qu.6.7.name=km/h -> m/s@ qu.6.7.question=To convert km/h into m/s, you should:@ qu.6.7.answer=3@ qu.6.7.choice.1=multiply by 1000 and multiply by 3600@ qu.6.7.choice.2=divide by 1000 and multiply by 3600@ qu.6.7.choice.3=multiply by 1000 and divide by 3600@ qu.6.7.choice.4=divide by 1000 and divide by 3600@ qu.6.8.mode=Multiple Choice@ qu.6.8.editing=useHTML@ qu.6.8.name=Speed of Sound -> mi/h@ qu.6.8.question=The speed of sound at room temperature is 340 m/s. What is the equivalent of this value in miles per hour (mi/h)?@ qu.6.8.answer=5@ qu.6.8.choice.1=167 mi/h@ qu.6.8.choice.2=324 mi/h@ qu.6.8.choice.3=423 mi/h@ qu.6.8.choice.4=584 mi/h@ qu.6.8.choice.5=761 mi/h@ qu.6.8.choice.6=942 mi/h@ qu.6.9.mode=Multiple Choice@ qu.6.9.editing=useHTML@ qu.6.9.name=Speed Limit - Foreign@ qu.6.9.question=A common highway speed limit in foreign country is 175,000 furlongs per fortnight. Given that one fortnight is 14 days and a furlong is 1/8 of a mile, what is this speed limit in mi/h@ qu.6.9.answer=4@ qu.6.9.choice.1=35 mi/h@ qu.6.9.choice.2=45 mi/h@ qu.6.9.choice.3=55 mi/h@ qu.6.9.choice.4=65 mi/h@ qu.6.9.choice.5=75 mi/h@ qu.6.9.choice.6=85 mi/h@ qu.7.topic=Ch 1, Sec 7 - Order of Magnitude Proablems@ qu.7.1.mode=Multiple Choice@ qu.7.1.editing=useHTML@ qu.7.1.name=Reach the Moon@ qu.7.1.question=How many Physics textbooks would you have to stack to reach the Moon?
@ qu.7.1.answer=3@ qu.7.1.choice.1=10⁴@ qu.7.1.choice.2=10⁷@ qu.7.1.choice.3=10¹⁰@ qu.7.1.choice.4=10¹³@ qu.7.1.choice.5=10¹⁴@ qu.7.2.mode=Multiple Choice@ qu.7.2.editing=useHTML@ qu.7.2.name=An Aquarium@ qu.7.2.question=An aquarium is $l yd long, $w yd wide and $h yd high. Approximately how many cans of soda will it take to fill the aquarium with the drink?@ qu.7.2.answer=2@ qu.7.2.choice.1=1.5 x 10³@ qu.7.2.choice.2=1.5 x 10⁸@ qu.7.2.choice.3=1.5 x 10¹³@ qu.7.2.choice.4=1.5 x 10¹⁸@ qu.7.2.choice.5=1.5 x 10²³@ qu.7.2.random= $l\=rand(79,83,3); $w\=rand(59,62,3); $h\=rand(9,12,3);@ qu.7.2.hint.1=A soda can could be considered a cylinder. The volume of a cylinder is V = pr²h, where r is the radius of the top (or the bottom) of the cylinder, and h is the height.@ qu.7.2.comment=A soda can could be considered a cylinder. The volume of a cylinder is V = pr²h, where r is the radius of the top (or the bottom) of the cylinder, and h is the height.@ qu.7.3.mode=Multiple Choice@ qu.7.3.editing=useHTML@ qu.7.3.name=CDs & Computer Case@ qu.7.3.question=How many compact disks would you have to stack on top of each other in order for the height of the stack to be equal to the one of a personal computer case?
@ qu.7.3.answer=2@ qu.7.3.choice.1=3 x 10¹@ qu.7.3.choice.2=3 x 10²@ qu.7.3.choice.3=3 x 10³@ qu.7.3.choice.4=3 x 10⁴@ qu.7.3.choice.5=3 x 10⁵@ qu.7.4.mode=Multiple Choice@ qu.7.4.editing=useHTML@ qu.7.4.name=Kleenex Tissues@ qu.7.4.question=How many Kleenex tissues would you have to place side by side in order to cover the entire surface of the Earth?@ qu.7.4.answer=2@ qu.7.4.choice.1=10¹³@ qu.7.4.choice.2=10¹⁶@ qu.7.4.choice.3=10¹⁹@ qu.7.4.choice.4=10²²@ qu.7.4.choice.5=10²⁵@ qu.7.4.hint.1=Surface area of a sphere is A = 4pr².@ qu.7.4.comment=Surface area of a sphere is A = 4pr².@ qu.7.5.mode=Multiple Choice@ qu.7.5.editing=useHTML@ qu.7.5.name=Tire Wear@ qu.7.5.question=How much of the tire tread is worn down after a single revolution of the wheel? Suppose that the average life of a tire is 65,000 miles.@ qu.7.5.answer=4@ qu.7.5.choice.1=2 x 10^-4m@ qu.7.5.choice.2=2 x 10^-6m@ qu.7.5.choice.3=2 x 10^-8m@ qu.7.5.choice.4=2 x 10^-10m@ qu.7.5.choice.5=2 x 10^-12m@ qu.7.5.hint.1=Calculate how many revolutions of the wheel there are in 65,000 miles.@ qu.7.5.hint.2=Circumference of a circle equals 2pr.@ qu.7.5.comment= 1. Calculate how many revolutions of the wheel there are in 65,000 miles.

2. Circumference of a circle equals 2pr.@ qu.7.6.mode=Multiple Choice@ qu.7.6.editing=useHTML@ qu.7.6.name=Heart Beats@ qu.7.6.question=What is the closest estimate of the number of times that a human heart beats in a lifetime?@ qu.7.6.answer=4@ qu.7.6.choice.1=2 x 10³@ qu.7.6.choice.2=2 x 10⁵@ qu.7.6.choice.3=2 x 10⁷@ qu.7.6.choice.4=2 x 10⁹@ qu.7.6.choice.5=2 x 10¹¹@ qu.7.6.choice.6=2 x 10¹³@ qu.8.topic=Ch 1, Sec 8 - Review Problems@ qu.8.1.mode=Randomized Formula@ qu.8.1.editing=useHTML@ qu.8.1.name=Garden of Flowers@ qu.8.1.question=The length of a rectangular garden of flowers is L = $l yd and its width is W = $w yd. What is its perimeter in inches (in)?@ qu.8.1.answer=$ans in (1 ? 0.05)@ qu.8.1.random= $l\=rand(10,20,3); $w\=rand(3,7,3); $ans\=sig(3, 36*2*($l+$w));@ qu.8.2.mode=Randomized Formula@ qu.8.2.editing=useHTML@ qu.8.2.name=Volume of the Earth@ qu.8.2.question=Assuming that the Earth is a perfect sphere, find its volume in $units. (Radius of the Earth is 6.37 x 10³km).@ qu.8.2.answer=$ans $units1 (1 ? 0.1)@ qu.8.2.random= $integer\=rint(5); $units\=switch($integer, "cm³", "in³", "yd³", "m³", "ft³"); $units1\=switch($integer, "cm^3", "in^3", "yd^3", "m^3", "ft^3"); $calculation\=switch($integer, 1.0827E27, 6.60702E25, 1.41611E21, 1.0827E21, 3.823511E22); $ans\=sig(3,$calculation)@ qu.8.2.hint.1=Volume of a sphere equals 4/3·pr³@ qu.8.2.comment=Volume of a sphere equals 4/3·pr³@ qu.8.3.mode=Randomized Formula@ qu.8.3.editing=useHTML@ qu.8.3.name=Increased Area of a Circle@ qu.8.3.question=If a radius of a circle is increased by $per%, what factor is its area increased by? Use 3 significant figures.@ qu.8.3.answer=$ans (1 ? 0.05)@ qu.8.3.random= $per\=rand(11,99,2); $ans\=sig(2, ((($per+100)/100)^2));@ qu.8.3.hint.1=The area of a circle equals pr².@ qu.8.3.comment=The area of a circle equals pr².

As radius increases, the area increases by that factor squared.@ qu.8.4.mode=Randomized Formula@ qu.8.4.editing=useHTML@ qu.8.4.name=Circumference@ qu.8.4.question=Find the circumference (in km) of 1/$fraction of a circle with the radius of $radius m. Give 3 significant figures.@ qu.8.4.answer=$ans km (1 ? 0.05)@ qu.8.4.random= $fraction\=rand(11,99,2); $radius\=rand(5, 99,3); $ans\=sig(3, 2*3.14*$radius/($fraction*1000));@ qu.8.4.hint.1=The circumference of a circle is 2pr.@ qu.8.4.comment=The circumference of a circle is 2pr.@ qu.8.5.mode=Randomized Formula@ qu.8.5.editing=useHTML@ qu.8.5.name=Pancake - Volume@ qu.8.5.question=What is the volume (in liters, l) of a pancake that is $thickness cm thick and has a radius of $radius cm? Give 2 significant figures.@ qu.8.5.answer=$ans l (1 ? 0.05)@ qu.8.5.random= $thickness\=rand(0.5,0.9,2); $radius\=rand(10,15,2); $ans\=sig(2,3.14*($radius)^2*$thickness*0.001);@ qu.8.5.hint.1=The pancake can be treated as a cylinder. Volume of a cylinder is pr²h, where r is the radius of the top (or the bottom of the cylinder) and h is the height.@ qu.8.5.comment=The pancake can be treated as a cylinder. Volume of a cylinder is pr²h, where r is the radius of the top (or the bottom of the cylinder) and h is the height.@ qu.8.6.mode=Randomized Formula@ qu.8.6.editing=useHTML@ qu.8.6.name=Cube - Diagonal@ qu.8.6.question=Find the larger diagonal (in terameters, Tm) of a cube that has a side of $side m.@ qu.8.6.answer=$ans Tm (1 ? 0.05)@ qu.8.6.random= $side\=rand(5,100,3); $ans\=sig(3,(3)^(1/2)*$side/10^12);@ qu.8.6.hint.1=

@ qu.8.6.hint.2=AB is the larger diagonal we are asked to find. AC is the length of the side of the cube and CB is the diagonal of the base of the cube. Use Pythagorean Theorem to find AB.@ qu.8.6.comment=

AB is the larger diagonal we are asked to find. AC is the length of the side of the cube and CB is the diagonal of the base of the cube. Use Pythagorean Theorem to find AB.@ qu.8.7.mode=Randomized Formula@ qu.8.7.editing=useHTML@ qu.8.7.name=Gigaseconds - Century@ qu.8.7.question=How many gigaseconds, Gs, are there in a $choice? Give 3 significant figures.@ qu.8.7.answer=$ans Gs (1 ? 0.1)@ qu.8.7.random= $integer\=rint(4); $choice\=switch($integer, "day", "year", "century", "millenium"); $calculation\=switch($integer, 8.64E-5, 0.031536, 3.1536, 31.536); $ans\=sig(3,$calculation)@ qu.8.8.mode=Randomized Formula@ qu.8.8.editing=useHTML@ qu.8.8.name=Volume of Air@ qu.8.8.question=What is the volume of air, in cubic feet, of a room whose dimensions are $l yd x $w yd x $h yd?@ qu.8.8.answer=$ans ft^3 (1 ? 0.05)@ qu.8.8.random= $l\=rand(7,10,3); $w\=rand(4,6.5,3); $h\=rand(2.9,3.9,3); $ans\=sig(3, 27*$l*$w*$h)@ qu.8.8.hint.1=When converting between cubic dimensions, the conversion factor must also be cubed.@ qu.8.8.comment=When converting between cubic dimensions, the conversion factor must also be cubed.@