Expert: Paul Klarreich - 9/24/2008

Question
QUESTION: ball thrown upward at 44ft/sec velocity. At certain ht. t in second, y = 44t-16t^2.
What is the instantaneous velocity at t = 2?

ANSWER: Questioner:   Ricardo
Category:  Calculus
Private:  No
 
Subject:  beginning calculus
Question:  ball thrown upward at 44ft/sec velocity. At certain ht. t in second, y = 44t-16t^2.
What is the instantaneous velocity at t = 2?
....................................................
Hi, Ricardo,

V at t = 2 is  y'(2).

y' = 44 - 32t

y'(2) = 44 - 32(2) = 44 - 64 = -20,

i.e. it is going DOWN at 20 ft/sec.


---------- FOLLOW-UP ----------

QUESTION: How did you get y(2)= 44-32(2)?
The equation is y = 44t - 16t(squared).

Answer
Questioner:   Ricardo
Category:  Calculus
Private:  No
 
Subject:  Velocity and acceleration
Question:  QUESTION: ball thrown upward at 44ft/sec velocity. At certain ht. t in second, y = 44t-16t^2.
What is the instantaneous velocity at t = 2?

ANSWER: Questioner:   Ricardo
Category:  Calculus
Private:  No

Subject:  beginning calculus
Question:  ball thrown upward at 44ft/sec velocity. At certain ht. t in second, y = 44t-16t^2.
What is the instantaneous velocity at t = 2?
....................................................
Hi, Ricardo,

V at t = 2 is  y'(2).

y' = 44 - 32t

y'(2) = 44 - 32(2) = 44 - 64 = -20,

i.e. it is going DOWN at 20 ft/sec.


---------- FOLLOW-UP ----------

QUESTION: How did you get y(2)= 44-32(2)?
The equation is y = 44t - 16t(squared).
..............................................

Sorry.  I meant to write:

y'(2)= 44-32(2), not  y(2).

Wait a minute -- I DID write y'(2).

Your I.V. at  t = 2 is the derivative, y', evaluated at t = 2.  That is what  y'(2) says.

If you are not familiar with derivatives, you have to tell me that.