Which speed is the fastest? (a) 70 mi / h (b) 140 km / h (c) 4.5 km / s (d) 48 mi / min

Name: Problem 75, Chapter 1: Introduction to General, Organic and Biochemistry
Uploaded: 2020-07-05T18:28:23-08:00
Duration: 3 min 37 s
Channel: John Barone
Description: Which speed is the fastest? (a) 70 mi / h (b) 140 km / h (c) 4.5 km / s (d) 48 mi / min

step 1 So this question asks us which speed is the fastest. And I'll put it up C here just to remember

Which speed is the fastest? (a) 70 mi / h (b) 140 km / h (c)...

Key Concepts

Dimensional Analysis

Dimensional analysis is a systematic approach used to check the consistency of equations and computations involving physical quantities by ensuring that the units on both sides match. It is a crucial tool for verifying that conversions and calculations, especially when dealing with different time and distance units, are done correctly.

Understanding Speed

Speed is a measure of how fast an object is moving, defined as the distance traveled per unit time. A clear understanding of speed and its units, such as distance per time (e.g., meters per second or miles per hour), is important for comparing and analyzing motion in various contexts.

Unit Conversion

This concept involves converting a measurement expressed in one unit to another unit using a conversion factor. It is essential when comparing physical quantities (like speed) that are given in different units, allowing them to be directly compared after being expressed in a common system.

Transcript

00:01 So this question asks us which speed is the fastest.

00:04 And i'll put it up c here just to remember to put the correct answer down here.

00:10 And so we have a, b, c, and d.

00:13 If you look at the numbers without doing any of the work first, just 70 miles per hour, 140 kilometers per hour, and then 4 .5 kilometers per second.

00:32 And then finally, 48 miles per minute.

00:40 What you may have noticed is that there are sort of two real big categories of speeds here.

00:47 A, b, c, d.

00:50 So a and b are speeds that you can attain in a car.

00:55 You certainly can drive a car 70 miles an hour.

00:57 And even if you didn't have a particularly good sense of how many kilometers go or in a mile, you might say well it's between one and two so at most you might think that this is 140 miles per hour and that's very fast for most cars but it's you probably have some sense it's a little bit less than that so you don't really need to do the conversions on on either these two because these are pretty slow look at this one see is 4 .5 kilometers per second right so even if you have some sense that a kilometers roughly a mile is one and a half kilometers, you go, that's really fast, right? you're going over a mile a second, a couple miles, three miles a second.

01:44 That's pretty fast.

01:45 And then down here, we have 48 miles per minute, right? so that's almost a mile a second, right? so before you do any conversions at all, it's clear that neither a nor b is going to be the fastest speed.

02:01 And even the sort of eyeball in it, you might be able to give.

02:04 Guess that it's going to be c.

02:06 Let's just do the conversions for c and d.

02:09 So this is 4 .5 kilometers first one second...

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