Calculus Summer Assignment..?

Question

My teacher has a sort of humor about him....

Upon completion of an AP Calculus Summer assignment, a group of disgruntled students chase their instructor to the top of a tower. They proceed to drop the evil math teacher from the tower. The position function (in feet) of the falling teacher at time t seconds is given by:
s(t)=-16t^2+128.
The velocity of the falling teacher at time t = a seconds is given by :
lim .. s(a) - s(t)
t->a ...... a - t
Find the velocity of the teacher when t = 2 seconds.

Help would be appreciated.

Well, I tried doing the problem, but my final answer was -32a. However, I don't think I'm supposed to receive an answer with a variable in it.

Dang, I almost had it finished, only one more step. Alright, thanks guys.

Answer 1

s(t)=-16t^2+128
diffrentiation would yieldthe velocity
s(t)=-32t
applying the limits
-32a-[-32(a-t)]
=-32a+32a-32t
=-32t
when t=2 then
s(t)=-32*2
=-64
i guess that would be the solution

Answer 2

lol
Don't you remember s=1/2 a t**2 and V=u+at?

Firstly, your s(t) formula has to be wrong. My guess is that the tower is 128 ft high, so
s(t)= 128 - 1/2.a.t**2 is the height above ground.
a = g, which i only know at 9.8metres/sec or 32.15ft/sec(?).

So s(2)=128 - 0.5 x 32.15 x 2 x 2= 63.9.

V=u+at = at, where U=0 = 32.15x2 = 64.3ft/sec

Stuffed if I can integrate the limit things. The lecturer put almost half the class to sleep during every lecture when I did it.

Answer 3

Velocity = v(t) = dS/dt
Thus:
v(t) = -32t

velocity when t = 2 seconds  v(2)
v(2) = -32(2) = -64 feet/second

So the velocity of the teacher when t = 2 seconds is -64 feet/second.

Answer 4

velocity is the derivative of distance function s(t)=-16t^2+128.
take the derivative and plug in 2 for t to get the answer.

ds/dt = -32t +0 @ t=2 sec velocity = 64 ft/sec

Answer 5

Wrong formula.
If the teacher was at rest before being dropped then the distance he falls is given by:

s(distance) = a/2(t^2)

for 1 second S= 16ft
2 64ft etc etc

Answer 6

y = x² Concavity is desperate with the aid of the 2d spinoff. locate the 2d spinoff. First, take the 1st spinoff. Then, take the spinoff of the 1st spinoff. Use the potential rule for the two (i will assume you comprehend a thank you to do this). First spinoff: y' = 2x 2d spinoff: y'' = 2 the 2d spinoff is two over the entire function. on the grounds it somewhat is useful 2 everywhere, the function would desire to be concave up everywhere. it is by technique of this rule: y'' = 0 ? try fails for concavity y'' > 0 ? concave upward y'' < 0 ? concave downward So the respond: The function is concave upward on (-?, ?) (i.e. everywhere) and concave downward nowhere. desire this facilitates! :)

Answer 7

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Answer 8

velocity, v , is ds / dt
v = - 32 t
v = - 64 ft / s after 2 seconds.