The accompanying table shows time-to-speed data for a 2004 Audi S4 Qauttro Cabriolet accelerating from rest to 130mph. How far had the Cabriolet traveled by the time it reached this speed? ( Use trapezoids to estimate the area under the velocity curve, but be careful: the time intervals vary in length.)

Question

shamil98 · Answer

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Speed Change:       Time:
Zero to                   (sec)
30 mph                   2.0
40 mph                   3.2                             
50 mph                   4.5
60 mph                   5.8
70 mph                   7.7
80 mph                   9.5
90 mph                   11.6
100 mph                 14.9
110 mph                 17.8 
120 mph                  21.7
130 mph                  26.3

nincompoop · Answer

have you tried diff methods of solving for the area yet?

shamil98 · Answer

Nope, gotta stick with trapezoids for this.

nincompoop · Answer

so how does the trapezoidal rule work?

shamil98 · Answer

$$T = \frac{ h }{ 2 } (y_0 + 2y_1 + 2y_2 +.... 2y_{n-1} + y_n)$$

nincompoop · Answer

then use it

shamil98 · Answer

$$h = \frac{ b-a }{ n }$$
n = the number of intervals.

nincompoop · Answer

i know what n stands for laughing out loud

nincompoop · Answer

$$\int\limits_{a}^{b}f(x) dx = (b-a)\left[ \frac{ (f(a)+f(b) }{ 2 } \right]$$

shamil98 · Answer

$$T = \frac{ 50 }{ 11 } (2 + 2(3.2) + 2(4.5) + 2(5.8) + 2(7.7) + 2(9.5) + 2(11.6) +2(14.9) $$
$$+ 2(17.8) + 2(21.7) + 26.3)$$

shamil98 · Answer

$$T = \frac{ 50 }{ 11 } (250) = \frac{ 12500 }{11 }$$
The answer from the book is 3340 ft.
So this method is wrong ..

nincompoop · Answer

multiple trapezoidal rule

timaashorty · Answer

No...

$$n= number of nuts you contain $$

shamil98 · Answer

The equation that the book solution uses is totally different from what I just did.

nincompoop · Answer

applying trapezoidal rule on each segment follows
$$\int\limits_{a}^{ b}f(x) dx =\frac{ b-a }{ 2n }\left[ f(a)+2\left\{ \sum_{i=1}^{n}f(a+ih) \right\}+f(b)\right]$$

shamil98 · Answer

I haven't learned that formula yet -.-

shamil98 · Answer

I'll prob just ask my teacher tomorrow thanks for helping nin.

nincompoop · Answer

or learn it on your own :P

nincompoop · Answer

if you can do the rectangles pretty well, I am sure trapezoid is not more difficult

nincompoop · Answer

what other rules have you learned if I may ask

shamil98 · Answer

Simpsons/trapezoidal, rectangle, cylinder i think thats about it.