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Chapter 1: Problem 32

A car is traveling at a speed of \(33 \mathrm{m} / \mathrm{s}\). (a) What is its speed in kilometers per hour? (b) Is it exceeding the \(90 \mathrm{km} /\) h speed limit?

Short Answer

Expert verified
The car's speed is approximately 118.8 km/h. Yes, it is exceeding the 90 km/h speed limit.

Step by step solution

01

Convert speed from meters per second to kilometers per hour

First, the speed in meters per second has to be converted to kilometers per hour. To convert from meters per second (m/s) to kilometers per hour (km/h), use the conversion factor 3.6. Hence, \( Speed (km/h) = Speed (m/s) * Conversion Factor \).
02

Speed calculation

Upon substituting the given speed and conversion factor, we have \( Speed (km/h) = 33 m/s * 3.6 = 118.8 km/h \)
03

Compare the calculated speed with the speed limit

The speed limit is 90 km/h. Comparing it with our calculated speed, 118.8 km/h, it's clear that the speed limit of 90 km/h is being exceeded. Hence, yes, the car is exceeding the speed limit.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Speed Conversion in Physics
Speed conversion is an essential concept in physics, particularly when discussing motion and transportation. It involves the change of units used to measure speed, such as converting meters per second (m/s) to kilometers per hour (km/h) or vice versa.

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Most popular questions from this chapter

Suppose \([\mathrm{V}]=\mathrm{L}^{3}, \quad[\rho]=\mathrm{ML}^{-3}, \quad\) and \([\mathrm{t}]=\mathrm{T} .\) (a) What is the dimension of \(\int \rho d V ?\) (b) What is the dimension of \(d V / d t ?\) (c) What is the dimension of \(\rho(d V / d t) ?\)

Consider the physical quantities \(s, v, a,\) and \(t\) with dimensions \([s]=\mathrm{L}, \quad[v]=\mathrm{LT}^{-1}, \quad[a]=\mathrm{LT}^{-2}, \quad\) and \([t]=\mathrm{T} . \quad\) Determine whether each of the following equations is dimensionally consistent. (a) \(v^{2}=2 a s ;\) (b) \(s=v t^{2}+0.5 a t^{2} ;(\mathrm{c}) v=s / t ;(\mathrm{d}) \quad a=v / t\).

A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

The following times are given using metric prefixes on the base SI unit of time: the second. Rewrite them in scientific notation without the prefix. For example, 47 Ts would be rewritten as \(4.7 \times 10^{13}\) s. (a) 980 Ps; (b) 980 fs; (c) 17 ns; (d) \(577 \mu\) s.

The purpose of this problem is to show the entire concept of dimensional consistency can be summarized by the old saying "You can't add apples and oranges." If you have studied power series expansions in a calculus course, you know the standard mathematical functions such as trigonometric functions, logarithms, and exponential functions can be expressed as infinite sums of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+\cdots\),where \(\begin{array}{llllll}\text { the } & a_{n} & \text { are } & \text { dimensionless } & \text { constants } & \text { for } & \text { all }\end{array}\) \(n=0,1,2, \cdots\) and \(x\) is the argument of the function. (If you have not studied power series in calculus yet, just trust us.) Use this fact to explain why the requirement that all terms in an equation have the same dimensions is sufficient as a definition of dimensional consistency. That is, it actually implies the arguments of standard mathematical functions must be dimensionless, so it is not really necessary to make this latter condition a separate requirement of the definition of dimensional consistency as we have done in this section.
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