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Ive tried numerous methods, but I cant seem to get this right. Please help, and explain step by step.
An object's position is given by x=bt+ct^3, where b=1.50m/s and c=0.640m/s3. To study the limiting process leading to the instantaneous velocity, calculate the object's average velocity over time intervals from 1.00 s to 3.00 s.
Also, from 1.95 s to 2.05 s.

Respuesta :

well, just for fun, let's see hat the form of the limit is 
v = dx/dt = b + 3 c t^2 
= 1.5 + 1.92 t^2 
========================= 
now 
from 1 to 3 
x(3)= 1.5*3 +.64*27=4.5+17.28 
= 21.78 
x(1) = 1.5+.64 = 2.14 
so 
x(3)-x(1) = 19.64 
delta t = 3 - 1 = 2 seconds 
so 
v during interval = 19.64/2 
= 9.82 m/s 
now check that with calculus v in the middle of that range 
v(2) =1.5+ 1.92 (4) = 9.18 m/s 
that makes sense, the parabola is headed up so the instant speed i the middle should be a bit less than average. 

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