A car is traveling at a speed of 33 m/s . (a) What is its speed in kilometers per hour? (b) Is i

A car is traveling at a speed of 33 m/s . (a) What is its...

Key Concepts

Unit Conversion

Unit conversion is the process of modifying a quantity expressed in one set of units to another set while maintaining the same physical quantity. It is essential in contexts where measurements need to be interpreted in different unit systems, such as converting meters per second to kilometers per hour.

Conversion Factor

A conversion factor is a multiplier used to change a measurement from one unit to another. In many speed conversions, a specific factor—like 3.6 when converting from meters per second to kilometers per hour—is applied to ensure accurate and consistent results.

Speed Measurement

Speed is the rate at which an object covers distance, typically quantified as distance per unit time. Understanding speed involves not only grasping the concept of movement but also correctly interpreting the units in which speed is expressed.

Comparison of Quantities

Comparing quantities involves evaluating numerical values to determine relationships such as equality or inequality. This concept is important in real-world applications like assessing whether a measured speed is within legal limits or exceeds them.

Transcript

00:02 Hello guys.

00:04 So we have this problem here where we're given the speed of a car.

00:08 It's 33 meters per second.

00:10 And we're given two parts.

00:12 First, can we convert it to kilometers per hour? and then is it going over the speed limit of 90 kilometers per hour? so let's start with the first part, converting it to kilometers per hour.

00:24 So this has less to do with physics and more just to do with unit conversion, but it's something very important in physics.

00:31 So let's do it.

00:33 So first, i have this rate.

00:38 And a rate can be written as a fraction.

00:42 I'm going to write it as a fraction.

00:46 33 meters are traveled for every one second that is lapsed.

00:53 So this is how it's written in a fraction.

00:56 So once we have it written in a fraction, we can manipulate the values so that we get kilometers per hour.

01:02 But we can't, in essence, change this value because we want this value to stay consistent when we convert it into kilometers per hour.

01:11 So what we got to do is use conversion ratios.

01:15 And what i mean by that? i mean, for every kilometer, how many meters are there? so there are 1 ,000 meters in one kilometer.

01:26 That's what the prefix kilo means.

01:28 So that means if i write the ratio of for every one kilometer, it is the same as 1 ,000 meters.

01:47 This fraction is essentially 1, if you think about it, because the denominator equals the numerator.

01:55 So this is a value of 1, and you're multiplying against this fraction, meaning the value is contained.

02:00 It is the same.

02:01 But why would i do it? what am i accomplishing here? if you look at the units, a property of these units is that if you have, if you divide a unit by itself, so like 33 meters divided by 1 ,000 meters, you're effectively canceling out the meters.

02:21 I don't have too much time to explain the intricacies of how to explain this, but basically just think of rates.

02:30 So if you have 33 meters per second, that's something you understand for every second.

02:34 Meter travels.

02:36 What if you do meters per meter? well, if you do meters per meter, that doesn't really make any sense.

02:43 It's just a value.

02:44 You're just finding a ratio, essentially, that has no units in essence.

02:50 So that means whenever you divide a unit by itself, you're effectively canceling it out.

02:58 So it's easier if you just memorize this and figure it out later.

03:01 So for now, just understand that if you have meters on the numerator and meters on the denominator, because after we multiply it and will, the meter unit will cancel out...

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