Posted by AP Physics on Saturday, June 13, 2009 at 1:12pm.
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. 212b 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^(n1) 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^(n1) 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  Anonymous, Saturday, June 13, 2009 at 3:33pm
In general
if f(x) = x^n
then d f(x)/dx = n x^(n1)
so
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
then
d f(t)/dt = 4.2 t
Now about that constant B
The slope of a constant is zero.
so
d/dt (A t^2 + B)
= 2 A t + 0
the end except to prove that d/dx (x^n) = n x^(n1)
f(x+dx) = (x+dx)^n
binomial expansion
(x+dx)^n = x^n + C(n,1) x^(n1) dx + C(n,2) x^(n2) (dx)^2 ....... +dx^n
C(n,k) = binomial coefficient
= n!/[(nk!) k!]
so for Cn,1)
C(n,1) = n!/[(n1)!] = n (lo and behold)
so
f(x+dx) = x^n + n x^(n1)dx + terms in dx^2 through dx^n
so
f(x+dx) f(x) = n x^(n1) dx + terms in dx^2 to dx^n
so
df(x)/dx = [f(x+dx)f(x)]/dx
as dx > 0
= n x^(n1)
f(x) = x^n
f

AP Physics  Damon, Saturday, June 13, 2009 at 3:37pm
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^(n1) but it is not a bad idea to know where the derivative comes from.
Answer This Question
Related Questions
 Math  In solving the eqaution(x+4)(x4),Eric stated thatthe solution would be x...
 PreCalculus  The question is "Find parametric equations for the line with the ...
 algebra  Explain in your own words what it means for an equation to model a ...
 Trig  Find an equation for the hyperbola described. Foci at (4,0) and (4,0); ...
 algebra  Write the equation of the line perpendicular to the given line and ...
 Algebra one, help me please?  Okay so, I have to write an equation in standard ...
 Physics  PLEASE HELP!! The x and y cooridinates of an object are given by x(t...
 Math  help please  Write the equation of a line that is perpendicular to the ...
 calculus  use implcit differenciation to find an eqaution of both the tangent ...
 Algebra  Please help me to solve this problem. Thank you in advance for helping...
More Related Questions