Question

1. the graph describes a child walking home from the library. describe the situation the graph represents.
2. bobby rides his bike up a long steep hill. he gets tired halfway up the hill and starts walking his bike up the hill. he then gets back on his bike, turns around, and races back down the hill to the bottom. sketch a qualitative graph to represent the situation.

Explanation:

Step1: Analyze the motion phases

Bobby's motion has three phases: riding up the hill (faster speed, steeper slope), walking up (slower speed, less steep slope), and racing down (faster speed, negative slope, steeper than riding up).

Step2: Sketch the graph

• Phase 1 (Riding up): Start at the origin (bottom of the hill), draw a line with a positive slope (steeper) as time (x - axis) and height (y - axis) increase.
• Phase 2 (Walking up): From the mid - point of the height, draw a line with a positive slope that is less steep than the first line (since walking is slower than riding).
• Phase 3 (Racing down): From the top of the hill (end of phase 2), draw a line with a negative slope (steeper than the first line) back to the y - value of the origin (bottom of the hill) as time increases.

Answer:

The graph should have three segments: a steeper positive - sloped segment (riding up), a less - steep positive - sloped segment (walking up), and a steeper negative - sloped segment (racing down) connecting the start (origin), mid - height, and back to the start's y - level. (A rough sketch description as above)