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Mathematics
Problem
A particle’s displacement is
s
(
t
)
=
ln
(
1
+
e
3
t
2
)
s(t)=\ln\bigl(1+e^{3t^{2}}\bigr)
s
(
t
)
=
ln
(
1
+
e
3
t
2
)
m. Its velocity at
t
=
1
s
t=1\,\text{s}
t
=
1
s
is a)
6
e
3
1
+
e
3
m/s
\dfrac{6e^{3}}{1+e^{3}}\;\text{m/s}
1
+
e
3
6
e
3
m/s
b)
6
1
+
e
3
m/s
\dfrac{6}{1+e^{3}}\;\text{m/s}
1
+
e
3
6
m/s
c)
3
e
3
1
+
e
3
m/s
\dfrac{3e^{3}}{1+e^{3}}\;\text{m/s}
1
+
e
3
3
e
3
m/s
d)
6
e
3
1
+
e
6
m/s
\dfrac{6e^{3}}{1+e^{6}}\;\text{m/s}
1
+
e
6
6
e
3
m/s
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