Question

1. chandler is taking a walk in the park. match each of the events listed below to the correct section of the graph.

chandler stops to look at a bird for 2.5 min
chandler is walking at 0.44 m/s
chandler stops for an ice cream cone for 5 min
chandler is walking at 0.17 m/s
a. at which time is chandler moving the fastest?
b. how far does chandler walk in the park?

1. leonard and sheldon are running a long distance race.

a. what is a possible explanation for sheldons line not starting at the origin?
b. who reaches the finish line first?
c. what is happening at point a?
d. who is running at a faster speed?
e. what is sheldons speed? leonards speed?

Explanation:

Step1: Analyze position - time graph for Chandler

In a position - time graph, a horizontal line means the object is at rest. The steeper the slope, the faster the speed. Speed $v=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position and $\Delta t$ is the change in time.

Step2: Match events to graph sections for Chandler

• Chandler stops to look at a bird for 2.5 min: This is a horizontal - line section. Let's assume section B is a short - duration stop, so it could be B.
• Chandler is walking at 0.44 m/s: A relatively steep non - horizontal line. Section A has a steeper slope, so it could be A.
• Chandler stops for an ice - cream cone for 5 min: A longer horizontal line. Section D is a long horizontal line, so it could be D.
• Chandler is walking at 0.17 m/s: A less steep non - horizontal line. Section C has a less steep slope, so it could be C.

Step3: Answer part a for Chandler

The steeper the slope of the position - time graph, the faster the speed. Section A has the steepest slope, so Chandler is moving the fastest during section A.

Step4: Answer part b for Chandler

The final position on the graph is the total distance walked. From the graph, the final position is 280 m (approximate reading from the y - axis at the end of the motion), so Chandler walks 280 m.

Step5: Analyze Leonard and Sheldon's graph

• For part a of Leonard and Sheldon's problem: A possible explanation for Sheldon's line not starting at the origin is that Sheldon had a head - start, meaning he started the race from a position ahead of the starting point (0,0).
• For part b: Sheldon reaches the finish line first as his line reaches the higher position (4 km) before Leonard's line.
• For part c: At point A, Leonard and Sheldon are at the same position, so they meet at point A.
• For part d: Sheldon has a steeper slope for most of the graph, so Sheldon is running at a faster speed.
• For part e: Sheldon's speed $v=\frac{\Delta x}{\Delta t}$. Sheldon covers a distance of 4 km in 25 min. First, convert 25 min to seconds: $t = 25\times60=1500$ s and $\Delta x = 4\times1000 = 4000$ m. Then $v=\frac{4000}{1500}=\frac{8}{3}\approx2.67$ m/s. Leonard covers 4 km in 35 min. Convert 35 min to seconds: $t = 35\times60 = 2100$ s. Then Leonard's speed $v=\frac{4000}{2100}=\frac{40}{21}\approx1.90$ m/s.

Answer:

• Chandler stops to look at a bird for 2.5 min: B
• Chandler is walking at 0.44 m/s: A
• Chandler stops for an ice - cream cone for 5 min: D
• Chandler is walking at 0.17 m/s: C
• a. Chandler is moving the fastest during section A
• b. Chandler walks 280 m
• 4a. Sheldon had a head - start
• 4b. Sheldon
• 4c. Leonard and Sheldon meet
• 4d. Sheldon
• 4e. Sheldon's speed is approximately 2.67 m/s, Leonard's speed is approximately 1.90 m/s