Question

Can someone please explain number 4 part D on this free response question: http://apcentral.collegeboard.com/apc/public/repository/ap10_frq_calculus_ab_formb.pdf

I have the answer, but I have no idea how to get it.
Thanks

Answer 1

the acceleration is given by the slope of the line, since it is the derivative of the velocity
so you need the slope of the line between the points \((7,20)\) and \((10,-10)\) for the first one

Answer 2

the easiest is distance
\[\Delta y\] = 30
the velocity = \[\Delta y / Delta t\] as to find the slope
10 m/s
as the slope is regular, velocity doesnt change, so a = 0 m/s2

Answer 3

the velocity is the like itself, so you need the equation for that line

Answer 4

@P0sitr0n if i am reading the quesion correctly, the graph is the graph of the velocity, so the acceleration between t = 7 and t = 10 is a constant, but it is not zero

Answer 5

Alright, so the equation for acceleration would be found using the mean value theorem: v(10)-v(7)/ 10-7 and I would look on the graph for v(10) and v(7).
I'm not sure what Poison means by his equation though.

Answer 6

oh, sorry, i thought y axis was distance

Answer 7

How would I find the equation for the position when all I have is a graph? Also, the equation for velocity is v'(9)(t-9) although I have no idea where the 9 came from.

Answer 8

well then i am lost because it looks like the slope is \(-10\)

Answer 9

These are the answers given, although they have no explanations http://apcentral.collegeboard.com/apc/public/repository/ap10_calculus_ab_form_b_sgs.pdf

Answer 10

you don't need the mean value theorem, it is just a line. slope of the line is -10 over 3, down 30

Answer 11

yes, satellite is right

Answer 12

ok so from the answer sheet we got that part right, \(a(t)=-10\)

Answer 13

velocity from 7 to 10 just measn the equation of that line. the slope is -10, and you have the point (7,10) so you can use the point - slope formula to find it

Answer 14

\[y-y_1=m(x-x_1)\]
\[y-20=-10(x-7)\]
\[y-20=-10x+70\]
\[y=-10x+90\] or in this case
\[v(t)=-10t+90\]

Answer 15

sorry i meant the slope is -10 and the point is (7,20)

Answer 16

That really helped! What about the position formula?

Answer 17

ok for the last one integrate the velocity, which we have above

Answer 18

\[v(t)=\int_7^t(-10t+90)dt+120\] and the 120 is there because that is how far you have gone from \(t=0\) to \(t=7\)

Answer 19

Would there be anyway to find the position function without integrating the velocity? I know how to do it, but if I was just asked for the position function in the future would I have to first find the velocity or could I find it quicker someother way?

Answer 20

actually what i wrote is not exacty rigth , we should use a dummy variable inside the integral

Answer 21

\[v(t)=\int_7^t(-10x+90)dx+120\]

Answer 22

and no, you have to integrate

Answer 23

Lastly, why is it the distance from 0 to 7 and not 0 to 10 or 7 to 10?

Answer 24

120 is the distance from 0 to 7 and since you want the total distance travelled you have to tack that on at the end

Answer 25

But the time interval is from 7 to 10?

Answer 26

question asks
and distance \(x (t )\) from building A that are valid for the time interval 7 < t < 10.

Answer 27

so it is asking for the total distance.
your formula is only valid on that interval, but it has to be the total distance

Answer 28

Thank you!

Answer 29

yw