91Ó°ÊÓ

Problem 43

(a) Estimate the average mass of a person's leg. (b) Estimate the length of a full-size school bus.

Problem 45

Estimate the number of automobile repair shops in the city you live in by considering its population, how often an automobile needs repairs, and how many cars each shop can service per day. Then look in the yellow pages of your phone directory to see how accurate your estimate is. By what percentage was your estimate off?

Problem 46

What is the order of magnitude of the number of seconds in one year?

Problem 47

What is the order of magnitude of the height (in meters) of a 40 -story building?

Problem 48

You have just performed an experiment in which you measured many values of two quantities, \(A\) and \(B\). According to theory, \(A=c B^{3}+A_{0} .\) You want to verify that the values of \(c\) and \(A_{0}\) are correct by making a graph of your data that enables you to determine their values from a slope and a vertical axis intercept. What quantities do you put on the vertical and horizontal axes of the plot?

Problem 50

A graph of \(x\) versus \(t^{4},\) with \(x\) on the vertical axis and \(t^{4}\) on the horizontal axis, is linear. Its slope is \(25 \mathrm{m} / \mathrm{s}^{4}\) and its vertical axis intercept is \(3 \mathrm{m} .\) Write an equation for \(x\) as a function of \(t\)

Problem 51

A patient's temperature was \(97.0^{\circ} \mathrm{F}\) at 8: 05 A.M. and \(101.0^{\circ} \mathrm{F}\) at 12: 05 P.M. If the temperature change with respect to elapsed time was linear throughout the day, what would the patient's temperature be at 3: 35 P.M.?

Problem 53

A physics student plots results of an experiment as \(v\) versus \(t .\) The equation that describes the line is given by \(a t=v-v_{0} .\) (a) What is the slope of this line? (b) What is the vertical axis intercept of this line?

Problem 54

A linear plot of speed versus elapsed time has a slope of $6.0 \mathrm{m} / \mathrm{s}^{2}\( and a vertical intercept of \)3.0 \mathrm{m} / \mathrm{s} .$ (a) What is the change in speed in the time interval between \(4.0 \mathrm{s}\) and \(6.0 \mathrm{s} ?\) (b) What is the speed when the elapsed time is equal to 5.0 s?

Problem 55

In a laboratory you measure the decay rate of a sample of radioactive carbon. You write down the following measurements: $$\begin{array}{lrrrrrrr} \hline \text { Time (min) } & 0 & 15 & 30 & 45 & 60 & 75 & 90 \\\ \text { Decays/s } & 405 & 237 & 140 & 90 & 55 & 32 & 19 \\\ \hline \end{array}$$ (a) Plot the decays per second versus time. (b) Plot the natural logarithm of the decays per second versus the time. Why might the presentation of the data in this form be useful?