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Mathematics
Problem
A particle’s position is given by
s
(
t
)
=
{
4
t
−
3
0
≤
t
≤
2
t
2
+
1
t
>
2
.
s(t)=\begin{cases}4t-3 & 0\le t\le 2\\ t^{2}+1 & t>2\end{cases}.
s
(
t
)
=
{
4
t
−
3
t
2
+
1
0
≤
t
≤
2
t
>
2
.
Explain why equality of the two pieces at
t
=
2
t=2
t
=
2
is necessary for the motion to represent a single uninterrupted trip along a line.
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