78. In this solution, we make use of the notation
x
(
t
) for the value of
x
at a particular
t
.
Thus,
x
(
t
) = 50
t
+ 10
t
2
with SI units (meters and seconds) understood.
(a) The average velocity during the first 3 s is given by
v
xx
t
avg
m/s.
=
−
=
+−
=
()
() ( )
30
5
0
3
1
0
3
0
3
80
2
Δ
(b) The instantaneous velocity at time
t
is given by
v
=
dx
/
dt
= 50 + 20
t
, in SI units. At
t
=
3.0 s,
v
= 50 + (20)(3.0) = 110 m/s.
(c) The instantaneous acceleration at time
t
is given by
a
=
dv
/
dt
= 20 m/s
2
. It is constant,
so the acceleration at any time is 20 m/s
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 Spring '06
 Stoler
 Physics, Derivative, Acceleration, International System of Units, Kilogram

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