AP Physics

posted by .

can you please explain this to me...

Were given this eqaution

x = At^2 + B

were A = 2.10 m/s^2
B = 2.80 m

ok and this is an example problem and it's wlking us through it

find the instantaneous velocity at t=t2=5.00s equlas the slope of the tangent to the curve at point P2 whoen in Fig. 2-12b and we could measure this slope off the gropah to obtain v2. we can calculate v more precisely, and for any time using the give formula

x = At^2 + B,

which is the engiene's position x at time t. Using the calculus formula for derivitves (THIS STEP I'M LOST)

(d/(dt))(Ct^n)= nCt^(n-1) and (dC)/(dt) = 0,

where C is any given constant, then

v = (dx)/(dt) = (d/(dt))(At^2 + B) = 2At.

We are given A = 2.10 m/s^2, so for t=t2=5.00s,

v2 = 2At = 2(2.10 m/s^2)5.00s = 21.0 m/s

ok it has been a long time sense I have taken calculus. I understand why instanteous velociy is equal to (dx)/(dt) but I do not understand this problem. Can you please explain it to me. I got lost were I wrote (THIS STEP I'M LOST)

I don't understand this
"(d/(dt))(Ct^n)= nCt^(n-1) and (dC)/(dt) = 0,

where C is any given constant, then

v = (dx)/(dt) = (d/(dt))(At^2 + B) = 2At."

Please explain to me the constant thing and what d is all by itself and what is dC and why they divide it by dt and how they got 2At

Thank you!

  • AP Physics -

    In general
    if f(x) = x^n
    then d f(x)/dx = n x^(n-1)
    if f(x) = x^2
    then d f(x)/dx = 2 x

    so if f(t) = t^2
    df(t)/dt = 2 t

    the constant multiple remains (three times the function has three times the slope) .
    if f(t) = 2.1 t^2
    d f(t)/dt = 4.2 t

    Now about that constant B
    The slope of a constant is zero.
    d/dt (A t^2 + B)
    = 2 A t + 0

    the end except to prove that d/dx (x^n) = n x^(n-1)

    f(x+dx) = (x+dx)^n
    binomial expansion
    (x+dx)^n = x^n + C(n,1) x^(n-1) dx + C(n,2) x^(n-2) (dx)^2 ....... +dx^n

    C(n,k) = binomial coefficient
    = n!/[(n-k!) k!]
    so for Cn,1)
    C(n,1) = n!/[(n-1)!] = n (lo and behold)
    f(x+dx) = x^n + n x^(n-1)dx + terms in dx^2 through dx^n

    f(x+dx) -f(x) = n x^(n-1) dx + terms in dx^2 to dx^n
    df(x)/dx = [f(x+dx)-f(x)]/dx
    as dx ---> 0
    = n x^(n-1)

    f(x) = x^n

  • AP Physics -

    Ignore the last two lines, I was thinking out loud.
    You may not need that proof at the end that d x^n/dx = n x^(n-1) but it is not a bad idea to know where the derivative comes from.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions


    I got this problem but its unrelated to any material that we worked on. Can some please help me to solve it and please explain it. Thanks Problem states: Given: x+(1/x)= square root of 3 PROVE: (x^13)+(1/(x^13))= square root of 3
  2. Physics

    PLEASE HELP!! The x and y cooridinates of an object are given by x(t) = 10t + 5t^2 + 3t^3 y(t) = 20t - 10t^2 + 2t^3 where x and y are in meters and t is in seconds. How fast is the object traveling at t = 1 s?
  3. Physics

    PLEASE HELP!! The x and y cooridinates of an object are given by x(t) = (10 m/s)t + (5 m/s2)t2 + (3 m/s3)t3 y(t) = (20 m/s)t - (10 m/s2)t2 + (2 m/s3)t3 where x and y are in meters and t is in seconds. What is the object's acceleration …
  4. Math

    In solving the eqaution(x+4)(x-4),Eric stated thatthe solution would be x+4=33=>x=29 or (x-4)=33=>x=37 However, at least one of these solutions fails to work when substituted back into the original eqaution. Why is that?
  5. algebra

    i do not understand how to solve for x and y can someone please explain it to me. an example of the problem i am workin on is 6x-4y=72
  6. Trig

    Find an equation for the hyperbola described. Foci at (-4,0) and (4,0); asymptote the line y= -x. Please explain the steps of this problem. My book does not get an example of this type of problem and I'm not having any luck working …
  7. algebra

    Explain in your own words what it means for an equation to model a real world situation an give an example. -it is right to say that when given a problem, we want to identify the quality of the problem we want to find, translate form …
  8. geometry/calculus

    Use Cavalieri's Principle to find the area of the region. In the example we see a "leaning tower" with base 'a' and height 'b'. The left side of the leaning rectangle is given by y = x^2, the right side given by y = (x - a)^2 the answer …
  9. Math Help

    could someone please give me an example not an example using coins, marbles, spinner, like something different that would explain the difference b/w theoretical and experimental probability. And please explain.
  10. Pre-Calculus

    The question is "Find parametric equations for the line with the given properties: Slope -2, passing through (-10, -20)." I don't even know where to begin, or what to do. Please help! This is an example problem, not the main homework …

More Similar Questions