Question

A sprinter knows that starting with an initial burst of speed gives her a velocity over time, t, of v(t) = 3.5t + 0.25t2 meters per second. If she saves her energy for the end of the race, she runs with a velocity of v(t) = 1.2t + 0.03t2. Which strategy will cover the greatest distance in a given time?
( Hint: Distance is the integral of velocity. )

How would i set up this equation?? D:

Answer 1

@newschoolgg do you think you could help me with integral equations again?? =(

Answer 2

I also saw someone else put up the same equation a while ago, but no one responded and they only put up 2/4 answer choices?
http://openstudy.com/study#/updates/529940c9e4b04e12f8228bcb

Answer 3

same question*

Answer 4

Looks like @tkhunny 's got this problem.

Answer 5

You DO have to start at \(t \ge 0\), otherwise you cheated!

\(\int\limits_{0}^{A}3.5\cdot t + 0.25\cdot t^{2}\;dt\)

\(\int\limits_{0}^{A}1.2\cdot t + 0.03\cdot t^{2}\;dt\)

"A" is the "given time". What I suggest you explore is whether this time makes a difference in the solution. I think it's obvious that A = 1 will favor the fast start and I would expect A = 200 to favor the slow start, but I would have to question the 0.25 parameter in the FAST Start. Are you sure that shouldn't be 0.025?

Answer 6

Yeah, i'm sure. I copy and pasted it write from my class.

and The options are:
a) She covers more distance in time, t, by waiting to put more energy into the end of the race.
b) Both strategies cover the same distance in time, t.
c) Insufficient information is given to compute the distances in each case.
d) She covers more distance in time, t, by starting with a burst of speed.

Would it be that there is not enough information because it doesn't say the time??

Answer 7

wwwooooowww how did i do that. *RIGHT

Answer 8

If the Fast Start Acceleration parameter (0.25) were less than the slow start acceleration parameter (0.03), then the time should make a difference. There would be a time over which they would be the same. Anything before that time would favor the fast start and any time after that would favor the slow start. That's why I suggested that .025 might be more appropriate.

As it is written, the fast start gets the immediate lead and then continue to accelerate faster throughout the race. This clearly favors the Fast Start in all cases.

In other words, if the parameters were reasonable, which they are not, there would be insufficient information. Since BOTH fast start parameters are superior to their corresponding slow start parameters (3.5 > 1.2 and .25 > .03), the FAST START is the clear victor in all cases.

You just have to think your way through it. No Guessing!!

Suomalainen?

Answer 9

im going to say its D right tkhunny?

Answer 10

I didn't say that? :-)

Answer 11

Note: This is an interesting question and a silly question. The interesting part is discussed above. The silly part is that sprinters are more interested in a fixed distance. Setting up a problem for a fixed time (even though we don't know what it is) is just a little odd.

Answer 12

so I was right or are u saying its B??

Answer 13

Asked and answered. Read the "Interesting" discussion carefully. It is clear, there. Feel free to ignore the part where I said it is a silly question. It is a silly question, but that doesn't help solve the problem AS IT IS WRITTEN.

Answer 14

confused *smacks head on brick wall*

Answer 15

lol

Answer 16

Just do the arithmetic. You will see that the Fast Start is ALWAYS ahead of the slow start. The second proposition is phrased poorly. "save her energy" is not reflected in the second equation, except to say that she NEVER gets around to a final sprint. I guess that's saving.