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In a time of t seconds, a particle moves a distance of s meters from its starting point, where s=6t^(2)+3 . (a) Find the average
In a time of
t
seconds, a particle moves a distance of
s
meters from its starting point, where
s=6t^(2)+3
.\ (a) Find the average velocity between
t=1
and
t=1+h
if:\ (i)
h=0.1
\ (ii)
h=0.01
\ (iii)
h=0.001
\ Enter the exact answers.\ (i) When
h=0.1
, the average velocity between
t=1
and
t=1+h
is
(m)/(sec)
.\ (ii) When
h=0.01
, the average velocity between
t=1
and
t=1+h
is
(m)/(sec)
.\ (iii) When
h=0.001
, the average velocity between
t=1
and
t=1+h
is
(m)/(sec)
.\ (b) Use your answers to part (a) to estimate the instantaneous velocity of the particle at time
t=1
.\ Round your estimate to the nearest integer.\ The instantaneous velocity appears to be
(m)/(sec)
.
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