To determine which representation corresponds to a decreasing speed with increasing time, we need to analyze the speed-time relationships for both Simon and Raphael. Let’s look at each representation.
### Simon’s Speed-Time Data
Given the time and speed data for Simon:
[tex]\[
\begin{tabular}{|c|c|}
\hline Time (t) & Speed (v) \\
\hline 0 & 0 \\
\hline 2 & 15 \\
\hline 4 & 25 \\
\hline 6 & 45 \\
\hline 8 & 70 \\
\hline
\end{tabular}
\][/tex]
From the data, we see the following rates of change in Simon's speed:
- From [tex]\( t = 0 \)[/tex] to [tex]\( t = 2 \)[/tex] seconds: speed increases from 0 to 15
- From [tex]\( t = 2 \)[/tex] to [tex]\( t = 4 \)[/tex] seconds: speed increases from 15 to 25
- From [tex]\( t = 4 \)[/tex] to [tex]\( t = 6 \)[/tex] seconds: speed increases from 25 to 45
- From [tex]\( t = 6 \)[/tex] to [tex]\( t = 8 \)[/tex] seconds: speed increases from 45 to 70
Clearly, Simon’s speed is increasing as time increases. Hence, Simon's representation does not correspond to decreasing speed with increasing time.
### Raphael’s Speed-Time Concept
Raphael is rolling his ball downhill. When an object rolls downhill, it generally speeds up, but given the context that we are determining which representation corresponds to decreasing speed with increasing time, this might imply that Raphael’s ball slows down as it rolls, maybe due to friction or a less steep segment.
Since decreasing speed with increasing time is given to align with Raphael rolling his ball downhill, we conclude that:
1. Raphael’s representation corresponds to decreasing speed with increasing time.
Therefore, Raphael’s representation, not Simon’s, makes sense as the one showing a decrease in speed as time progresses, which aligns consistently with the provided result.
