Welcome Back To Calculus
by theorangedog on Jan.02, 2008, under Skills
Problem:
A rock thrown upward with velocity 16 ft/sec reaches height 
at time t.
(a) Find its average speed 
from 
to 
.
(b) Find its average speed from to 
.
(c) What is 
at ?
Solution:
To find speed given distance, we need to take the first derivative. Derivatives of polynomials are one of the few things I remember, even though this is covered in the material I’m reading. That equation is: 
. However, the question isn’t asking for a limit, so the full equation of 
should be used. Essentially, it is the average of the first derivative at two given points.
This results in:
(a) 8 ft/sec
(b) -8 ft/sec
(c) 0, as it is the instantaneous point of reversal (this one assumes a limit, as t approaches 
)
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