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To check your answer, consider the following:
(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:
which are obviously not the desired units of km/h.
(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km/h and we have indeed obtained these units.
(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km/hr does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is defined to be 60 minutes, so the precision of the conversion factor is perfect.
(4) Next, check whether the answer is reasonable. Let us consider some information from the problem—if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.
Solution for (b)
There are several ways to convert the average speed into meters per second.
(1) Start with the answer to (a) and convert km/h to m/s. Two conversion factors are needed—one to convert hours to seconds, and another to convert kilometers to meters.
(2) Multiplying by these yields
Discussion for (b)
If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.
You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module Accuracy, Precision, and Significant Figures will help you answer these questions.
While there are numerous types of units that we are all familiar with, there are others that are much more obscure. For example, a firkin is a unit of volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary or encyclopedia to research different “weights and measures.” Take note of any unusual units, such as a barleycorn, that are not listed in the text. Think about how the unit is defined and state its relationship to SI units.
Some hummingbirds beat their wings more than 50 times per second. A scientist is measuring the time it takes for a hummingbird to beat its wings once. Which fundamental unit should the scientist use to describe the measurement? Which factor of 10 is the scientist likely to use to describe the motion precisely? Identify the metric prefix that corresponds to this factor of 10.
The scientist will measure the time between each movement using the fundamental unit of seconds. Because the wings beat so fast, the scientist will probably need to measure in milliseconds, or ${\text{10}}^{-3}$ seconds. (50 beats per second corresponds to 20 milliseconds per beat.)
One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?
The fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on the measure of a centimeter.
Identify some advantages of metric units.
The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?
A car is traveling at a speed of $\text{33 m/s}$ . (a) What is its speed in kilometers per hour? (b) Is it exceeding the $\text{90 km/h}$ speed limit?
Show that $1\text{.}\text{0 m/s}=3\text{.}\text{6 km/h}$ . Hint: Show the explicit steps involved in converting $1\text{.}\text{0 m/s}=3\text{.}\text{6 km/h.}$
$\frac{\text{1.0 m}}{\mathrm{s}}=\frac{1\text{.}\text{0 m}}{\mathrm{s}}\times \frac{\text{3600 s}}{\text{1 hr}}\times \frac{\mathrm{1\; km}}{\text{1000 m}}$
$=3\text{.}\text{6 km/h}$ .
American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)
Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)
length: $\text{377 ft}$ ; $4\text{.}\text{53}\times {\text{10}}^{3}\text{in}\text{.}$ width: $\text{280ft}$ ; $3\text{.}3\times {\text{10}}^{3}\text{in}$ .
What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)
Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)
$8\text{.}\text{847 km}$
The speed of sound is measured to be $\text{342 m/s}$ on a certain day. What is this in km/h?
Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?
(a) $1\text{.}3\times {\text{10}}^{-9}\text{m}$
(b) $\text{40 km/My}$
(a) Refer to [link] to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?
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