Question

Check my work for average speed using calculus.

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Answer 1

Peicewise

Intervals
0-2 2-4 4-8 8-12
equations
2 x -2x x
ads up to

4 +6+48+40 = 98

98/12(the time)

Answer 2

nice

Answer 3

When I say adds up to, I mean I took the integral.

Answer 4

Right idea, but you didn't include the negative sign when you evaluated the 4-8 interval. It dramatically changes the result.

Answer 5

there is an easier way since this involves no curves, just straight lines

however, the functions you integrated, you forgot about the y_intercepts of the lines
-2x+12 and x-12

Answer 6

I took the absolute value integral of the equations. Was I not supposed to do that?

Answer 7

no lines beneath axis represent neg velocity

Answer 8

Oh, I'm sorry, it's look for speed, not velocity. You should be correct then.

Answer 9

(Velocity incorporates direction, so you have to subtract negative velocities from your average velocity over a time period. Speed is just rate of movement independent of direction, so it doesn't matter if velocity is positive or negative.)

Answer 10

So, I'm correct?

Answer 11

I believe so.

Answer 12

i get 26/12 = 13/6

Answer 13

Area under curve from 0 to 6 is 14
Area of triangle from 6 to 12 is 12

since we assume pos speed, add the areas and divide by 12

Answer 14

hmm...

Answer 15

plus 98/12 = 8.1
the velocity never was greater than 4 so how can avg be 8.1 ?

Answer 16

Could you explain in some more detail how you got 13/6?

Answer 17

\[avg = \frac{1}{12}[\int\limits_{0}^{2}2dx + \int\limits_{2}^{4}x dx+\int\limits_{4}^{6}(12-2x) dx+\int\limits_{6}^{8}(2x-12) dx+\int\limits_{8}^{12}(12-x) dx]\]

Answer 18

Cow is right, I feel dumb for not actually doing the math myself. The problem is twofold - first, the equations you used to describe the graph aren't accurate (2 and x are right, but try evaluating -2x at 4 and see what happens), and you need to integrate the positive and negative sections of the graph separately because you need to take absolute values of the negative terms.

I got this:
From 0-2, y=2
From 2-4, y=x
From 4-6 and 6-8, y=-2x+12
From 8-12, y=-4+x

Now integrate these equations over these 5 intervals and add the absolute values together and see what you get.

Answer 19

or don't use calculus at all, break it down into triangles and rectangles
simple areas
integral is just the area under a curve right

Answer 20

D'oh! I realize why I got it wrong. I forgot to add 12 and - 4! Thanks guys!

Answer 21

This is a connected question. Based on this question, I'd say that this is false. I just want to make sure. It looks pretty easy.