Question

on may 26, 1934, a streamlined, stainless - steel diesel train called the zephyr set the worlds nonstop long - distance speed record for trains. its run from denver to chicago took 13 hours, 4 minutes, 58 seconds, and was witnessed by more than a million people along the route. the total distance traveled was 1633.8 km. what was its average speed in km/h? what was its average speed in m/s?

Explanation:

Step1: Convert time to hours

First, convert 4 minutes and 58 seconds to hours. 4 minutes is $\frac{4}{60}$ hours and 58 seconds is $\frac{58}{3600}$ hours.
The total time $t_{h}$ in hours is $13+\frac{4}{60}+\frac{58}{3600}$.
$13+\frac{4}{60}+\frac{58}{3600}=13 + 0.0667+0.0161=13.0828$ hours.

Step2: Calculate average speed in km/h

The formula for average speed $v$ is $v=\frac{d}{t}$, where $d$ is distance and $t$ is time. Given $d = 1633.8$ km and $t=t_{h}=13.0828$ hours.
$v_{km/h}=\frac{1633.8}{13.0828}\approx125$ km/h.

Step3: Convert distance to meters and time to seconds

The distance $d$ in meters is $d = 1633.8\times1000 = 1633800$ m.
The time $t_{s}$ in seconds is $13\times3600+4\times60 + 58=46800+240+58 = 47098$ s.

Step4: Calculate average speed in m/s

Using the formula $v=\frac{d}{t}$, with $d = 1633800$ m and $t = t_{s}=47098$ s.
$v_{m/s}=\frac{1633800}{47098}\approx34.7$ m/s.

Answer:

125 km/h
34.7 m/s