mean velocity using integration

[yohanson77]

Hello again.

I have this one:

Q. The velocity 'V' m/s of a missile fired from a launcher varies with the horizontal distance 'X' kilometers according to the eqaution:

V=6X-X^2

Using integration determine the mean velocity of the missile as it travels from X=0 to X=6 kilometers.

I have so far:

V= Limit(inter(X)/6-0 dx

=Limit(inter 6X-X^2/6 dx

=1/6(Limit(inter 6X-X^2 dx

So far......sorry if it does not make sence, inter(integrate)

Thanks

Yohanson

 

[skeeter]

something is not right ... max velocity of a missile is only 9 m/s? that's only about 20 mph.

you sure you have correctly provided all the given information regarding units?

 

[stapel]

I'm not sure what you're doing with the "velocity" formula...?

Has your class covered "average value of a function" yet? If not, try here or here for an explanation. Once you've studied what's going on, you'll see what is almost-certainly intended for this exercise (namely, integrate over the interval to find the total "area", and then divide by the "width" to get the average "height").

Eliz.

 

[yohanson77]

All Info is correct

Hi Skeeter,
I've checked the question and all the info is correct. I done a question yesterday and it had a vehicle weighing 39,000 tonnes, that I would like to see.

yours

yohanson

 

[Deleted member 4993]

Hello again.

I have this one:

Q. The velocity 'V' m/s of a missile fired from a launcher varies with the horizontal distance 'X' kilometers according to the eqaution:

V=6X-X^2

Using integration determine the mean velocity of the missile as it travels from X=0 to X=6 kilometers.

I have so far:

V= Limit(inter(X)/6-0 dx

=Limit(inter 6X-X^2/6 dx

=1/6(Limit(inter 6X-X^2 dx

So far......sorry if it does not make sence, inter(integrate)

Thanks

Yohanson

You have to first integrate the expression - then apply the limit - then divide by 6

Average velocity = 1/6 int[0 to 6][6x-x^2] dx

= 1/6 * [0 to 6][3x^2 - x^3/3]

= 1/6 * [{3*36 - 216/3} - {0}]

= 6