The speed limit on some interstate highways is roughly 100 km / h . (a) What is this in meters p

The speed limit on some interstate highways is roughly 100...

Key Concepts

Unit Conversion

Unit conversion is the process of changing one unit of measurement to another using conversion factors. This is a fundamental skill in science and engineering that ensures all quantities are expressed in compatible units, making calculations, comparisons, and communication clearer and more accurate.

Conversion Factors

Conversion factors are numerical ratios that express how many of one unit are equal to another unit. They are used to systematically convert measurements between contiguous unit systems, such as the metric system and the imperial system, ensuring that the physical quantity remains unchanged.

Metric to SI Conversion

Converting from kilometers per hour to meters per second involves understanding that the metric system is based on powers of ten. Since 1 kilometer is equivalent to 1000 meters and 1 hour is equivalent to 3600 seconds, one divides the kilometer-per-hour value by 3.6 to obtain the speed in meters per second.

Imperial System Conversion

Converting a metric speed to miles per hour requires the use of conversion factors between the metric and imperial systems. Specifically, one uses the fact that 1 kilometer is approximately 0.621371 miles. This allows for a direct conversion between kilometers per hour and miles per hour, ensuring measurements are appropriately expressed in the desired unit system.

Transcript

00:05 All right, so in this problem, we are being asked to convert 100 kilometers per hour to meters per second in a and miles per hour in b.

00:21 So the way we start with our unit conversion is we will write out our 100 kilometers per hour.

00:30 But rather than writing it like that, in the interest of being able to convert it later, we will actually rewrite it as 100 kilometers per as a fraction one hour.

00:45 That way as we go through our conversions we can sort of cancel out the units in the numerator and denominator get the units that we want.

00:52 So for part a we're being asked to find meters per second.

00:56 So we need to convert the numerator into meters from kilometers and to hours into seconds for the denominator.

01:05 So as you would do with conversions, you start multiplying and you multiply the conversion factor for the numerator and then the denominator.

01:12 So for example, we want to cancel out kilometers here, so we'll put kilometers in the denominator and we'll put meters in the numerator.

01:22 And so one kilometer is 1 ,000 meters, so kilo meaning 1 ,000.

01:28 That then cancels out kilometers and so we are left with meters in the numerator.

01:38 So now we have to convert the denominator from hours to seconds.

01:44 So once again we'll do the same thing.

01:45 We want to cancel out hours from the denominator.

01:48 So we put hours up top here and so one hour is going to be 60 minutes and then again we'll convert minutes to seconds.

01:58 So one minute, is 60 seconds and that does it...

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