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GreyNoise
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Homework Statement
I am stumped on a problem (number 13 page 49) from the Serway/Vuille/Faughn text
College Physics 8th Ed. The problem is
A person takes a trip driving with a constant speed of 88.5 km/h, except for a 22 min rest stop.
If the person's average speed is 77.8 km/h, how much time is spent on the trip and how far does
the person travel?
Homework Equations
The answer is 2.80 hours and 218 km (from back of book and 218/2.80 = 77.8). I can't even reverse
engineer the problem from the answer. Presumably all I need are the GT's
\begin{array}{cll}
x_2 & = & x_1 + v_1t + \frac{1}{2}at^2 \\
&&\\
x_2 & = & \displaystyle x_1 + v_{ave}t \\
&&\\
v_{ave} & = & \displaystyle\frac{v_1 + v_2}{2} \\
&&\\
v_2 & = & \displaystyle v_1 + at \\
&&\\
v_2^2 - v_1^2 & = & \displaystyle 2a(x_2 - x_1) \\
\end{array}
The Attempt at a Solution
For all of these, I keep coming back to the two unknowns (for me anyway) t and x (distance). I tried
assuming an acceleration from the rest stop to back on the road again,
[itex]a = \frac{0+88.5}{0.367}[/itex][itex]\frac{km}{h^2}[/itex], where 0.367 h = 22 mins
I thought that v2 = v1 + at might lead to segmenting the problem into before and after the rest stop,
but that got me nowhere (I have been reduced to guessing, so I would have been surprised had it worked);
I tried leveraging the other velocity by
[itex]v_{ave}[/itex] = 77.8 [itex]\frac{km}{h} = \frac{88.5 - v_{other}}{2}[/itex][itex]\frac{km}{h}[/itex]
which left me with vother= 66.1 km/h and wondering what the hell that really meant to the problem anyway.
Can anyone recommend a solution or just a hint (I'll take either) to this problem for me? The book's examples do
not cover anything quite like this that I have read (and reread).
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