Differences
This shows you the differences between two versions of the page.
| Next revision | Previous revision | ||
| 183_notes:examples:averagevelcompare [2014/07/10 20:10] – created caballero | 183_notes:examples:averagevelcompare [2014/07/10 20:23] (current) – [Solution] caballero | ||
|---|---|---|---|
| Line 6: | Line 6: | ||
| ==== Setup ==== | ==== Setup ==== | ||
| + | |||
| + | You will compare the two ways of computing the average velocity using the information provided and any information that you can collect or assume. | ||
| === Facts ==== | === Facts ==== | ||
| Line 11: | Line 13: | ||
| * The distance from East Lansing to Chicago is 3.58$\times10^5m$. | * The distance from East Lansing to Chicago is 3.58$\times10^5m$. | ||
| * For the first hour (3600 s), you drive at 24.6 $\dfrac{m}{s}$. | * For the first hour (3600 s), you drive at 24.6 $\dfrac{m}{s}$. | ||
| - | * For the next 2.5 hours (9000 s), you drive at 66.8 $\dfrac{m}{s}$. | + | * For the next 2.5 hours (9000 s), you drive at 29.9 $\dfrac{m}{s}$. |
| === Lacking === | === Lacking === | ||
| Line 26: | Line 28: | ||
| * The average velocity is given by $v_{avg,x} = \dfrac{\Delta x}{\Delta t}$. | * The average velocity is given by $v_{avg,x} = \dfrac{\Delta x}{\Delta t}$. | ||
| - | * The // | + | * The // |
| - | + | ||
| ==== Solution ==== | ==== Solution ==== | ||
| + | |||
| + | For this situation, the average velocity can be computed, | ||
| + | |||
| + | $$v_{avg,x} = \dfrac{\Delta x}{\Delta t} = \dfrac{3.58\times10^5m}{3600 s + 9000 s} = 28.4 \dfrac{m}{s}$$ | ||
| + | |||
| + | You can compare that to the // | ||
| + | |||
| + | $$v_{avg,x} \approx \dfrac{v_i + v_f}{2} = \dfrac{24.6 \dfrac{m}{s} + 29.9 \dfrac{m}{s}}{2} = 27.3 \dfrac{m}{s}$$ | ||
| + | |||
| + | You can see that the // | ||
| + | |||
| + | $$\Delta x = v_{avg,x} \Delta t = 27.3 \dfrac{m}{s} (3600s+9000s) = 3.43\times10^5 m = 343 km$$ | ||
| + | |||
| + | which is leaves you at the " | ||