Floating Down the River

Learning Focus

Read and build graphs of motion: distance vs. time, speed as slope, and stops.

Big idea

On a distance–time graph:

• Slope = speed (distance ÷ time).
• A steeper segment means faster movement.
• A horizontal segment means not moving.
• A downward segment means moving back toward the start.

For a segment, speed $=\dfrac{\Delta d}{\Delta t}$.

Worked example

A raft floats $3$ mph for $2$ hours, rests for $1$ hour, then floats $2$ mph for $3$ hours.

• Segment 1: $3\cdot2=6$ mi
• Segment 2: $0$ mi (flat)
• Segment 3: $2\cdot3=6$ mi
• Total: $12$ mi in $6$ hours

A graph through $(1,4)$ and $(3,12)$ has speed $\dfrac{12-4}{3-1}=4$ mph.

Takeaways

• Slope is speed; flat is stopped.
• Total distance is the sum over each segment.
• Graph stories should be read left to right.