This question was on my physics exam this morning. For some reason, I couldn't actually get the right answer (I felt quite stupid for it too). So lets see how you do TWW.

Given the position function x(t) = 4t -3(t^2), where x is in meters and t is measured in seconds, what is the average velocity from t = 0 seconds to t = 4 seconds

Possible Choices:
a) -11 m/s
b) 11 m/s
c) -5 m/s
d) 5 m/s
e) -14 m/s


[GO]

4/30/2009 12:59:05 PM

f) all of the above

4/30/2009 12:59:57 PM

yeah this is why we come here

to do math

get fucked

4/30/2009 1:00:39 PM

^well hey, a 3rd grade problem was posted in here, i figured I'd post something I was curious about that was more on our "level"

4/30/2009 1:01:35 PM

hmmm I woulda thought -8 m/s but I must be wrong

4/30/2009 1:02:13 PM

i get -12 m/s

4/30/2009 1:02:16 PM

^^I too thought -8 m/s...

I'm going to have words with the proffessor.

[Edited on April 30, 2009 at 1:03 PM. Reason : .]

4/30/2009 1:03:05 PM

ibtmsh

4/30/2009 1:03:41 PM

v(t) = 4-6t
v(0) = 4
v(4) = -20

(-20-4)/2 = -12

[Edited on April 30, 2009 at 1:05 PM. Reason : post how you get -8]

4/30/2009 1:04:18 PM

i got -8, but i don't remember if im doin it right

derivative of x(t) is the function for velocity right?

x(t)=4t-3t²
x'(t)=4-6t

solve for t=0;t=4 and take the avg to get -8?

4/30/2009 1:05:50 PM

-8 m/s

Neuse, your average is wrong, it should be (-20+4)/2

4/30/2009 1:06:00 PM

yeh I forgot to derive the velocity equation...still doesn't give an answer on the sheet...

thanks makes sense now...

[Edited on April 30, 2009 at 1:07 PM. Reason : ...]

4/30/2009 1:06:21 PM

lol yeah, -8 m/s is right



[Edited on April 30, 2009 at 1:08 PM. Reason : halfway between 4 and -20 is -8]

4/30/2009 1:07:06 PM

(vf - vi) / 2 = (-20-4)/2 = -12

[Edited on April 30, 2009 at 1:09 PM. Reason : 1]

4/30/2009 1:07:14 PM

i had some classes once where you were given a few answer choices and the teacher said to pick the one closest to what you got (i think it was statics)

4/30/2009 1:07:22 PM

^ statics was like that for me too...but for this one -11 and -5 would both be equally as far away

4/30/2009 1:08:22 PM

c

4/30/2009 1:08:54 PM

closest w/o going over then?

4/30/2009 1:09:19 PM

The Price is Right, Bob...

4/30/2009 1:09:32 PM

Using the approach where you take the derivative to get velocity, you divide by 2 because the velocity is linear in time, so to get the average velocity you can just take the average of the initial and final velocities.

Or the third-grader approach to the problem which is just as valid would be to take the difference of the position at time 0 (0), the position at time 4 (-32), then divide by the time it took to travel that distance. -32/4 = -8.

4/30/2009 1:10:32 PM

are you accusing my brain of acting like a 3rd grader?

4/30/2009 1:11:43 PM

^lol

^^ I did that too, only I threw in some integration signs while at it...
Yeah, I just e-mailed Dr. Mowat to see what he has to say. I swear it's an error on the exam. I circled -11 m/s, just because I know my chances of getting it right could be 1/3 (I know the avg. velocity can't be positive...)

Quote :

"The Price is Right, Bob Drew ..."

Fixed it for you...

[Edited on April 30, 2009 at 1:15 PM. Reason : .]

4/30/2009 1:12:45 PM

I get -10.6, so a)-11 would make sense

whats the answer?

4/30/2009 1:15:10 PM

^ wtf. how?

4/30/2009 1:16:05 PM

I just plugged in the t-value into the equation (0,1,2,3,4) took the answers, added them all together and divided by 5

I think the numbers I got for x were, 0, 1, -4, -15, -35

average was -10.6

4/30/2009 1:17:40 PM

Oh son of a bitch. GG

4/30/2009 1:19:33 PM

[Edited on April 30, 2009 at 1:20 PM. Reason : fluke double post. sry admins]

4/30/2009 1:19:33 PM

actually, that wasnt right, I wrote down -35 instead of -32, so the average goes down to -10m/s

I still wouldve put down -11 since it was closest

4/30/2009 1:20:23 PM

Quote :

"Fixed it for you... "

F that...it's never going to be the same

Quote :

"Oh son of a bitch. GG"

at least if he is right, you put the right answer

[Edited on April 30, 2009 at 1:21 PM. Reason : ...]

4/30/2009 1:20:51 PM

True...

4/30/2009 1:22:47 PM

Quote :

"I just plugged in the t-value into the equation (0,1,2,3,4) took the answers, added them all together and divided by 5 I think the numbers I got for x were, 0, 1, -4, -15, -32 average was -10 "

Thats what I did.

4/30/2009 1:24:10 PM

yeah, I guess if you broke the integrals down even further, like 0.25 or 0.5, you would get a more exact answer

and I'm sure if you did some integration bullshit you would get the exact answer. Its been a good 7-8 years since I took physics or calculus, so I dont do that crazy math anymore, haha

4/30/2009 1:27:25 PM

can you just take all the integers into account (and not the decimels)? i guess if you did all the integers and the zero (0,1,2,3,4) and also the in-betweens (0,½,1,...4) maybe it all converges to a number closer to -11

4/30/2009 1:27:43 PM

^^ hahahah, I like this guy!

I integrated the equation to get "2(t^2)-(t^3)" and divided by b-a (4-0=4).

[2(4^2)-(4^3)]/[4-0] = (32-64)/4 = -8 m/s

I like DROD's method the best. I was going to do that until I had this flashback of calculus class and getting yelled at for using antiquated methods.

[Edited on April 30, 2009 at 1:28 PM. Reason : ^ probably.]

4/30/2009 1:27:56 PM

Well I did the integration. It's no different.

I got an A+ in Calc III. I'm going to end up getting a damn B in pys 205 though.

[Edited on April 30, 2009 at 1:30 PM. Reason : .]

4/30/2009 1:30:11 PM

Quote :

"I just plugged in the t-value into the equation (0,1,2,3,4) took the answers, added them all together and divided by 5 I think the numbers I got for x were, 0, 1, -4, -15, -35 average was -10.6"

that cant be right. you found the position at each second but dividin them by 5 makes it some weird avg position or somethin.

-8 FTW

[Edited on April 30, 2009 at 1:32 PM. Reason : FTW]

4/30/2009 1:31:39 PM

I'm getting -8 as well.

4/30/2009 1:31:44 PM

I get -8 m/s as well. But I'm not an expert

4/30/2009 1:31:53 PM

yeah, I used to overthink things waaay too much in college, and would second guess my answers/methods when taking tests

I guess now that I'm out and am not exposed to all the superfluous math stuff, I dumb things down a bit. I dont know if thats a good thing or a bad thing

hell I dont even know if what I did here is right

4/30/2009 1:32:04 PM

The correct answer is -8 m/s.

All of the available answers are wrong.

This is not a calculus problem. I tutor middle school math on the side, and this is a question that could very easily be asked to my Algebra students.

Of course you can use calculus, but there just isn't any reason to.

Quote :

"Using the approach where you take the derivative to get velocity, you divide by 2 because the velocity is linear in time, so to get the average velocity you can just take the average of the initial and final velocities."

The average velocity is NOT the average of the final and initial velocities. That is asinine.

The average velocity is (Total Distance / Total Time).

And that is simply [x(4) - x(0)] / 4.

Your professor is an idiot, or you wrote the problem here differently than it was on the test.

[Edited on April 30, 2009 at 1:35 PM. Reason : a]

4/30/2009 1:32:40 PM

Quote :

"because the velocity is linear in time"

4/30/2009 1:34:50 PM

^^that just happened

4/30/2009 1:35:46 PM

The plane takes off

4/30/2009 1:38:03 PM

wouldnt it be pointless to take the velocity at 0 seconds? There is no velocity at that point...

4/30/2009 1:39:24 PM

the equation isn't for an object starting from rest, i dont think

4/30/2009 1:40:21 PM

well x(0) = 0...

dammit, I should be working and not thinking about this crap all afternoon

4/30/2009 1:41:58 PM

^That's the position at time = 0 not the velocity.

4/30/2009 1:46:05 PM

Position equation = 4t - 3(t^2)
Velocity equation = 4 - 6t
Acceleration equation = -6

Average velocity = Integral of velocity equation (position equation) from a to b divided by b - a
Average velocity = Integral of 4 - 6t from 0 to 4 divided by 4-0
which is [4(4) - 3(4^2) - (4(0) - 3(0^2))]/(4-0) = [16 - 48 - (0)]/4 = -32/4 = -8

Your professor is wrong. The plane takes off. Third grade is now super complicated. No, we're not playing fucking stonehenge. I changed lanes without signaling while running a red light and speeding.

THE ANSWER IS NEGATIVE FUCKING EIGHT.

4/30/2009 1:59:15 PM

haha, he probably wrote down the wrong damn question

4/30/2009 2:02:25 PM

set em up

4/30/2009 2:02:58 PM