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Mathematics
Mathematics
Problem
For the displacement
s
(
t
)
=
1
+
4
t
3
m
s(t)=\sqrt{1+4t^{3}}\,\text{m}
s
(
t
)
=
1
+
4
t
3
m
, the velocity
v
(
t
)
v(t)
v
(
t
)
equals a)
12
t
2
1
+
4
t
3
\dfrac{12t^{2}}{\sqrt{1+4t^{3}}}
1
+
4
t
3
12
t
2
b)
6
t
2
1
+
4
t
3
6t^{2}\sqrt{1+4t^{3}}
6
t
2
1
+
4
t
3
c)
6
t
2
1
+
4
t
3
\dfrac{6t^{2}}{\sqrt{1+4t^{3}}}
1
+
4
t
3
6
t
2
d)
6
t
2
(
1
+
4
t
3
)
3
/
2
\dfrac{6t^{2}}{(1+4t^{3})^{3/2}}
(
1
+
4
t
3
)
3/2
6
t
2
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